id stringlengths 6 8 | alias stringlengths 24 50 | problem stringlengths 24 5.03k | answer int64 -16,384 80.2B | graph stringlengths 0 6.44k | domain stringclasses 4
values | secondary_domain stringclasses 4
values | goal stringclasses 4
values | evaluator_id stringclasses 1
value | root_lemma stringclasses 89
values | lemma_paths listlengths 0 5 | recipe_id stringlengths 0 6 | seed_template_id stringclasses 96
values | ending_id stringclasses 13
values | olympiad_level int64 2 9 | num_spawns int64 0 3 ⌀ | lemma_set listlengths 1 7 ⌀ | num_lemmas int64 1 7 ⌀ | generation_time float64 0 43.9 | created_at stringlengths 27 27 | verification dict | problem_hash stringlengths 6 6 | parent_id stringlengths 0 6 | variant stringclasses 3
values | license stringclasses 1
value | llm_solvers listlengths 1 13 ⌀ | solution_status int64 0 2 ⌀ | lemma_applicability listlengths 0 12 | irt_difficulty dict |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
a71abb | nt_num_divisors_compute_v1_865884756_3435 | Let $S$ be the set of all ordered pairs $(x,y)$ of positive integers such that $xy = 25000000$. Define $n$ to be the minimum value of $x + y$ over all such pairs. Compute the number of positive divisors of $n$. | 25 | graphs = [
Graph(
let={
"n": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Const(25000000)))), expr=Sum(Var("x"), Var("y")))),
"result": NumD... | NT | null | COMPUTE | sympy | B3 | [
"B3"
] | 0cd20d | nt_num_divisors_compute_v1 | null | 4 | 0 | [
"B3"
] | 1 | 0.002 | 2026-02-08T17:23:46.264371Z | {
"verified": true,
"answer": 25,
"timestamp": "2026-02-08T17:23:46.266249Z"
} | b345a8 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 105,
"completion_tokens": 916
},
"timestamp": "2026-02-18T02:18:53.916Z",
"answer": 25
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
1944a0 | nt_count_digit_sum_v1_1431428450_1182 | Let $n$ be a positive integer. Define $A$ as the set of all prime numbers $n$ such that $2 \leq n \leq 104723$. Let $k$ be the number of elements in $A$. Compute the number of positive integers $n$ such that $1 \leq n \leq k$ and the sum of the decimal digits of $n$ is equal to 15. | 592 | graphs = [
Graph(
let={
"_n": Const(2),
"upper": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Ref("_n")), Leq(Var("n"), Const(104723)), IsPrime(Var("n"))))),
"target_sum": Const(15),
"result": CountOverSet(set=SolutionsSet(var=Var("n... | NT | null | COUNT | sympy | COUNT_PRIMES | [
"COUNT_PRIMES"
] | 07c874 | nt_count_digit_sum_v1 | null | 4 | 0 | [
"COUNT_PRIMES"
] | 1 | 0.369 | 2026-02-08T13:56:27.861059Z | {
"verified": true,
"answer": 592,
"timestamp": "2026-02-08T13:56:28.229915Z"
} | 8ff7d6 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 133,
"completion_tokens": 2141
},
"timestamp": "2026-02-15T22:10:09.780Z",
"answer": 592
},
{
... | 1 | [
{
"lemma": "COUNT_PRIMES",
"status": "ok"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -5.49,
"mid": 0.22,
"hi": 6.51
} | ||
c03dbf | modular_mod_compute_v1_124444284_6754 | Let $a=32761$. Among all ordered pairs $(x,y)$ of positive integers satisfying
$$x+y=96,$$
let $m$ be the maximum possible value of $xy$.
Let $r$ be the remainder when $a$ is divided by $m$.
Consider all ordered pairs $(x,y)$ of positive integers satisfying
$$xy = 10896601.$$
For each such pair, form the sum $x+y$. L... | 6,373 | graphs = [
Graph(
let={
"_m": Const(2),
"_n": Const(72307),
"a": Const(32761),
"m": MaxOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Sum(Var("x")... | NT | null | COMPUTE | sympy | B3 | [
"B3/MAX_PRIME_BELOW",
"B1"
] | 6af13a | modular_mod_compute_v1 | affine_mod | 7 | 0 | [
"B1",
"B3",
"MAX_PRIME_BELOW"
] | 3 | 0.004 | 2026-02-08T08:37:22.148055Z | {
"verified": true,
"answer": 6373,
"timestamp": "2026-02-08T08:37:22.151867Z"
} | ee3654 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 214,
"completion_tokens": 1930
},
"timestamp": "2026-02-13T20:09:15.881Z",
"answer": 6373
},
{... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok_later"
},
{
... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
d1e849_n | alg_linear_system_2x2_v1_1218484723_771 | A cryptographic system iteratively applies the function $f(x) = x^2 - 637 \bmod 1849$ to a starting value $a$. Values of $a$ from 0 to 1848 are tested. A value is special if it returns to itself after exactly 5 iterations but not before. Let $A$ be the set of such values. The size of $A$ helps compute a determinant use... | 61,471 | ALG | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM/POLY_ORBIT_HENSEL"
] | 007af8 | alg_linear_system_2x2_v1 | null | 7 | null | [
"LIN_FORM",
"POLY_ORBIT_HENSEL"
] | 2 | 0.033 | 2026-02-25T02:30:45.517625Z | null | 372788 | d1e849 | narrative | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 1,
"correct": {
"strict": false,
"boxed": false,
"relaxed": true
},
"usage": {
"prompt_tokens": 364,
"completion_tokens": 32768
},
"timestamp": "2026-03-30T15:56:27.128Z",
"answer": null
},
{
... | 1 | [
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "POLY_ORBIT_HENSEL",
"status": "ok_later"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": 1.5,
"mid": 4.69,
"hi": 7.23
} | |
0b0b4d | comb_count_partitions_v1_717093673_2378 | Let $n$ be the number of positive integers $n_1$ such that $1 \leq n_1 \leq 321$ and $n_1 \equiv \left\lfloor \frac{n_1}{2} \right\rfloor \pmod{7}$. Determine the value of the number of integer partitions of $n$. | 89,134 | graphs = [
Graph(
let={
"_n": Const(321),
"n": CountOverSet(set=SolutionsSet(var=Var("n1"), condition=And(Geq(Var("n1"), Const(1)), Leq(Var("n1"), Ref("_n")), Congruent(a=Var(name='n1'), b=Floor(arg=Div(left=Var(name='n1'), right=Const(value=2))), modulus=Const(value=7))))),
... | NT | COMB | COUNT | sympy | L3C | [
"L3C"
] | 73f8b0 | comb_count_partitions_v1 | null | 7 | 0 | [
"L3C"
] | 1 | 0.002 | 2026-02-08T16:47:34.867183Z | {
"verified": true,
"answer": 89134,
"timestamp": "2026-02-08T16:47:34.868982Z"
} | 3630e5 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 118,
"completion_tokens": 1135
},
"timestamp": "2026-02-17T12:25:25.512Z",
"answer": 89134
},
... | 1 | [
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "L3C",
"status": "ok"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
abe99f | diophantine_fbi2_count_v1_1439011603_1081 | Let $k$ be the number of integers $t$ in the range $36 \leq t \leq 2229$ for which there exist positive integers $a$ and $b$ with $1 \leq a \leq 39$, $1 \leq b \leq 156$, and $$t = 21a + 9b + 6.$$ Let $S$ be the set of integers $d$ such that $2 \leq d \leq 71$, $d$ divides $k$, and $$5 \leq \frac{k}{d} \leq 74.$$ Compu... | 13 | graphs = [
Graph(
let={
"k": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=39)), Geq(left=Var(name='b'), right=Const(value=... | NT | null | COUNT | sympy | COUNT_FIB_DIVISIBLE | [
"LIN_FORM"
] | 7b2633 | diophantine_fbi2_count_v1 | null | 5 | 0 | [
"COUNT_FIB_DIVISIBLE",
"LIN_FORM"
] | 2 | 0.153 | 2026-02-08T15:54:21.706675Z | {
"verified": true,
"answer": 13,
"timestamp": "2026-02-08T15:54:21.859733Z"
} | d1d13f | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 180,
"completion_tokens": 3797
},
"timestamp": "2026-02-16T15:41:18.407Z",
"answer": 13
},
{
... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
125e3e | lin_form_endings_v1_1080341949_298 | Let $a = 20$ and $b = 70$. Define $g = \gcd(a, b)$, $a' = \left\lfloor \frac{a}{g} \right\rfloor$, and $b' = \left\lfloor \frac{b}{g} \right\rfloor$. Let $A = 9$ and $B = 13$. Compute the value of $$
5214 \cdot \left(a' \cdot A + b' \cdot B - a' \cdot b'\right) \mod 72828.
$$ | 58,362 | graphs = [
Graph(
let={
"a_coeff": Const(20),
"b_coeff": Const(70),
"A_val": Const(9),
"B_val": Const(13),
"g_step": GCD(a=Ref("a_coeff"), b=Ref("b_coeff")),
"ap_node": Floor(Div(Ref("a_coeff"), Ref("g_step"))),
"bp_node": F... | COMB | NT | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | lin_form_endings_v1 | null | 3 | null | [
"LIN_FORM"
] | 1 | 0.001 | 2026-02-08T13:24:58.899296Z | {
"verified": true,
"answer": 58362,
"timestamp": "2026-02-08T13:24:58.900295Z"
} | 2d0335 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 162,
"completion_tokens": 701
},
"timestamp": "2026-02-15T14:52:17.753Z",
"answer": 58362
},
{... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V8_SUM",
"s... | {
"lo": -5.49,
"mid": 0.22,
"hi": 6.51
} | ||
3409f9 | comb_sum_binomial_row_v1_1742523217_4861 | Let $d$ be the smallest integer greater than or equal to 2 that divides 1356277. Compute $2^d$. | 8,192 | graphs = [
Graph(
let={
"_n": Const(2),
"n": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Ref("_n")), Divides(divisor=Var("d"), dividend=Const(1356277))))),
"result": Pow(Const(2), Ref("n")),
},
goal=Ref("result"),
)
] | NT | null | SUM | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR"
] | bc3776 | comb_sum_binomial_row_v1 | null | 2 | 0 | [
"MIN_PRIME_FACTOR"
] | 1 | 0.002 | 2026-02-08T09:19:25.134804Z | {
"verified": true,
"answer": 8192,
"timestamp": "2026-02-08T09:19:25.136883Z"
} | 809a2f | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 75,
"completion_tokens": 460
},
"timestamp": "2026-02-14T02:40:09.943Z",
"answer": 8192
},
{
... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V7",
"status": "no... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
40f59a | nt_sum_gcd_range_mod_v1_1874849503_1060 | Let $N$ be the minimum value of $x + y$ over all ordered pairs $(x, y)$ of positive integers such that $x \cdot y = 1024144$. Let $k$ be the number of positive integers $t$ such that $27 \le t \le 1140$ and there exist positive integers $a \le 45$ and $b \le 40$ satisfying $t = 12a + 15b$. Define
$$
\text{sum} = \sum_{... | 43,927 | graphs = [
Graph(
let={
"_n": Const(87918),
"N": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Const(1024144)))), expr=Sum(Var("x"), Var("y")... | NT | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM",
"B3"
] | 688dbe | nt_sum_gcd_range_mod_v1 | null | 6 | 0 | [
"B3",
"LIN_FORM"
] | 2 | 0.18 | 2026-02-08T13:32:39.120627Z | {
"verified": true,
"answer": 43927,
"timestamp": "2026-02-08T13:32:39.300202Z"
} | 087454 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 294,
"completion_tokens": 7174
},
"timestamp": "2026-02-11T07:52:48.366Z",
"answer": 43927
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "V7",
... | {
"lo": -5.48,
"mid": 0.74,
"hi": 7.52
} | ||
d54b8e_n | comb_catalan_compute_v1_1218484723_7343 | A theater company stages a sequence of 11 performances, each either a play or a musical, such that at no point do musicals outnumber plays in the schedule. The number of valid schedules is the 11th Catalan number. If the company earns $5944$ dollars per such schedule over a special festival, compute the remainder when ... | 25,487 | COMB | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM",
"STARS_BARS"
] | 05793e | comb_catalan_compute_v1 | affine_mod | 3 | null | [
"LIN_FORM",
"STARS_BARS"
] | 2 | 0.038 | 2026-02-25T08:44:58.434085Z | null | 762eab | d54b8e | narrative | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 187,
"completion_tokens": 1408
},
"timestamp": "2026-03-31T02:13:24.831Z",
"answer": 25487
},
{
"... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "STARS_BARS",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "n... | {
"lo": -5.37,
"mid": 0.23,
"hi": 5.22
} | |
3a7512 | comb_catalan_compute_v1_655260480_4820 | Let $n$ be the number of integers $t$ such that $10 \leq t \leq 21$ and there exist positive integers $a$ and $b$ with $1 \leq a \leq 5$, $1 \leq b \leq 2$, and $t = 2a + 3b + 5$. Compute the $n$-th Catalan number. | 16,796 | graphs = [
Graph(
let={
"n": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=5)), Geq(left=Var(name='b'), right=Const(value=1... | COMB | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | comb_catalan_compute_v1 | null | 3 | 0 | [
"LIN_FORM"
] | 1 | 0.003 | 2026-02-08T18:07:39.631035Z | {
"verified": true,
"answer": 16796,
"timestamp": "2026-02-08T18:07:39.633607Z"
} | 7e1fae | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 128,
"completion_tokens": 1548
},
"timestamp": "2026-02-18T14:09:13.024Z",
"answer": 16796
},
... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no... | {
"lo": -3.12,
"mid": 1.47,
"hi": 6.57
} | ||
870ab7 | modular_mod_compute_v1_458359167_1887 | Let $a$ be the smallest value of $x + y$ over all ordered pairs $(x, y)$ of positive integers such that $x \cdot y = 4937284$. Compute the remainder when $a$ is divided by $34225$. | 4,444 | graphs = [
Graph(
let={
"a": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Const(4937284)))), expr=Sum(Var("x"), Var("y")))),
"m": Const(3422... | NT | null | COMPUTE | sympy | B3 | [
"B3"
] | 0cd20d | modular_mod_compute_v1 | null | 6 | 0 | [
"B3"
] | 1 | 0.002 | 2026-02-08T04:55:28.626129Z | {
"verified": true,
"answer": 4444,
"timestamp": "2026-02-08T04:55:28.628464Z"
} | 92e59b | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 164,
"completion_tokens": 1703
},
"timestamp": "2026-02-11T22:27:15.253Z",
"answer": 4444
},
{
"i... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
}
] | {
"lo": -3.45,
"mid": 1.15,
"hi": 6.18
} | ||
584dcd | nt_count_divisors_in_range_v1_397696148_1607 | Let $n = 277200$. Determine the number of positive divisors $d$ of $n$ such that $19 \leq d \leq 6164$. Find the value of this count. | 135 | graphs = [
Graph(
let={
"n": Const(277200),
"a": Const(19),
"b": Const(6164),
"result": CountOverSet(set=SolutionsSet(var=Var("d"), condition=And(Divides(divisor=Var("d"), dividend=Ref("n")), Geq(Var("d"), Ref("a")), Leq(Var("d"), Ref("b"))))),
},
... | NT | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | nt_count_divisors_in_range_v1 | null | 4 | 0 | [
"LIN_FORM"
] | 1 | 0.141 | 2026-02-08T12:39:36.457148Z | {
"verified": true,
"answer": 135,
"timestamp": "2026-02-08T12:39:36.598591Z"
} | bf7a47 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 88,
"completion_tokens": 2429
},
"timestamp": "2026-02-15T04:01:26.018Z",
"answer": 135
},
{
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
}
] | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
e3955f | nt_count_coprime_and_v1_1915831931_473 | Compute the number of positive integers $n$ such that $1 \leq n \leq 14539$, $\gcd(n, 7) = 1$, and $\gcd(n, 9) = 1$. | 8,308 | graphs = [
Graph(
let={
"upper": Const(14539),
"k1": Const(7),
"k2": Const(9),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("upper")), Eq(GCD(a=Var("n"), b=Ref("k1")), Const(1)), Eq(GCD(a=Var("n... | NT | null | COUNT | sympy | C3 | [
"C3/MAX_PRIME_BELOW",
"ONE_PHI_1"
] | 8716c3 | nt_count_coprime_and_v1 | null | 4 | 0 | [
"C3",
"MAX_PRIME_BELOW",
"ONE_PHI_1"
] | 3 | 17.321 | 2026-02-08T15:28:31.055695Z | {
"verified": true,
"answer": 8308,
"timestamp": "2026-02-08T15:28:48.376291Z"
} | f61142 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 92,
"completion_tokens": 851
},
"timestamp": "2026-02-16T07:10:45.092Z",
"answer": 8308
},
{
... | 1 | [
{
"lemma": "C3",
"status": "ok"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok_later"
},
{
"lemma": "ONE_PHI_1",
"status": "ok"
}... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
265058 | sequence_count_fib_divisible_v1_153355830_75 | Let $u$ be the sum of $\phi(d)$ over all positive divisors $d$ of $908$. Compute the number of positive integers $n \le u$ such that the $n$th Fibonacci number is divisible by $13$. | 129 | graphs = [
Graph(
let={
"upper": SumOverDivisors(n=Const(value=908), var='d', expr=EulerPhi(n=Var(name='d'))),
"d": Const(13),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("upper")), Divides(divisor=Ref("d"... | NT | null | COUNT | sympy | ONE_PHI_2 | [
"K3"
] | 54c41e | sequence_count_fib_divisible_v1 | null | 6 | 0 | [
"K3",
"ONE_PHI_2"
] | 2 | 0.1 | 2026-02-08T02:52:59.593166Z | {
"verified": true,
"answer": 129,
"timestamp": "2026-02-08T02:52:59.693348Z"
} | ae9955 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 161,
"completion_tokens": 2242
},
"timestamp": "2026-02-10T11:45:25.883Z",
"answer": 129
},
{
"id... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
... | {
"lo": -1.77,
"mid": 0.38,
"hi": 2.41
} | ||
488e39 | algebra_quadratic_discriminant_v1_784195855_7244 | Let $a = 2$, $b = 4$, and $c = -96$. Let $S$ be the set of all ordered pairs $(x_1, x_2)$ of positive odd integers such that $x_1 + x_2 = 4$. Let $e$ be the number of elements in $S$, and define $D = b^{e} - 4ac$.
Let $r = 2$ if $D > 0$, and $r = 0$ otherwise. Additionally, let $r = r + 1$ if $D = \sum_{k=\binom{19}{... | 50,882 | graphs = [
Graph(
let={
"_n": Const(95317),
"a": Const(2),
"b": Const(4),
"c": Const(-96),
"D": Sub(Pow(Ref("b"), CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x1"), Var("x2")]), condition=And(IsPositive(arg=Var(name='x1')), IsPositive(arg... | COMB | null | COMPUTE | sympy | BINOMIAL_ALTERNATING | [
"BINOMIAL_ALTERNATING",
"ZERO_BINOM_N",
"COMB1"
] | 0427c6 | algebra_quadratic_discriminant_v1 | null | 3 | 0 | [
"BINOMIAL_ALTERNATING",
"COMB1",
"ZERO_BINOM_N"
] | 3 | 0.004 | 2026-02-08T09:09:58.723894Z | {
"verified": true,
"answer": 50882,
"timestamp": "2026-02-08T09:09:58.727789Z"
} | ca9082 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 283,
"completion_tokens": 1298
},
"timestamp": "2026-02-24T10:35:17.334Z",
"answer": 50782
},
{
... | 1 | [
{
"lemma": "BINOMIAL_ALTERNATING",
"status": "ok"
},
{
"lemma": "COMB1",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma"... | {
"lo": -3.84,
"mid": -1.67,
"hi": 1.32
} | ||
642d8c | diophantine_fbi2_min_v1_153355830_575 | Let $m = 8$. Let $T$ be the set of positive integers $n$ such that $1 \leq n \leq 10$ and $n \equiv 0 \pmod{5}$. Let $s = \sum_{n \in T} 1$, and let $g = \gcd(m, s)$. Compute $\sum_{d \mid g} \mu(d)$, where $\mu$ is the M\"obius function. Let $P$ be the set of all ordered pairs $(i, j)$ of positive integers such that $... | 3 | graphs = [
Graph(
let={
"_m": Const(8),
"_n": Const(3),
"k": Const(120),
"upper": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=Eq(GCD(a=Var("i"), b=Var("j")), SumOverDivisors(n=GCD(a=Ref(name='_m'), b=SumOverSet(set=Solutio... | NT | null | EXTREMUM | sympy | COUNT_FIB_DIVISIBLE | [
"SUM_DIVISIBLE/MOBIUS_COPRIME/COUNT_COPRIME_GRID"
] | 3d3aeb | diophantine_fbi2_min_v1 | null | 6 | 0 | [
"COUNT_COPRIME_GRID",
"COUNT_FIB_DIVISIBLE",
"MOBIUS_COPRIME",
"SUM_DIVISIBLE"
] | 4 | 0.059 | 2026-02-08T03:10:21.209819Z | {
"verified": true,
"answer": 3,
"timestamp": "2026-02-08T03:10:21.269052Z"
} | 738d82 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 340,
"completion_tokens": 715
},
"timestamp": "2026-02-18T08:01:07.511Z",
"answer": 3
}
] | 2 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "ok_later"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K5",
"stat... | {
"lo": -10,
"mid": -6.47,
"hi": -2.95
} | ||
4de11d | nt_min_coprime_above_v1_168721529_1191 | Let $m$ be the smallest integer $d \ge 2$ that divides $2562485641$. Let $n_0$ be the smallest integer $n$ such that $83521 < n \le 83754$ and $\gcd(n, m) = \sum_{d\mid\gcd(5,7)} \mu(d)$, where $\mu$ is the M\"obius function. Compute $n_0$. | 83,522 | graphs = [
Graph(
let={
"_n": Const(2),
"start": Const(83521),
"upper": Const(83754),
"modulus": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Ref("_n")), Divides(divisor=Var("d"), dividend=Const(2562485641))))),
"result": M... | NT | null | EXTREMUM | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR",
"MOBIUS_COPRIME"
] | 604469 | nt_min_coprime_above_v1 | null | 7 | 0 | [
"MIN_PRIME_FACTOR",
"MOBIUS_COPRIME"
] | 2 | 0.026 | 2026-02-08T13:31:22.404395Z | {
"verified": true,
"answer": 83522,
"timestamp": "2026-02-08T13:31:22.430737Z"
} | 528da1 | CC BY 4.0 | [
{
"id": 4,
"model": "NousResearch/Hermes-4-405B",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 150,
"completion_tokens": 402
},
"timestamp": "2026-02-10T03:24:34.266Z",
"answer": 83522
},
... | 1 | [
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "MOBIUS_COPRIME",
"status": "ok"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "n... | {
"lo": -6.69,
"mid": -2.39,
"hi": 1.92
} | ||
508660 | antilemma_sum_factor_cartesian_v1_784195855_2937 | Let $p$ and $q$ be positive integers. Define $N$ to be the number of positive integers $p$ such that there exists a positive integer $q$ with $p < q$, $pq = 36$, and $\gcd(p, q) = 1$. Let $S$ be the set of ordered pairs $(i, j)$ such that $1 \leq i \leq 6$ and $1 \leq j \leq 13$. Define $x = \sum_{(i,j) \in S} i \cdot ... | 1,911 | graphs = [
Graph(
let={
"_n": Const(79194),
"x": SumOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=EulerPhi(n=CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Var(name='p')), Exists(var=Var(name='q'), condition=And(... | NT | null | COMPUTE | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS/ONE_PHI_2/SUM_FACTOR_CARTESIAN",
"SUM_FACTOR_CARTESIAN"
] | 0bec54 | antilemma_sum_factor_cartesian_v1 | null | 5 | 0 | [
"COPRIME_PAIRS",
"ONE_PHI_2",
"SUM_FACTOR_CARTESIAN"
] | 3 | 0.001 | 2026-02-08T06:08:02.411663Z | {
"verified": true,
"answer": 1911,
"timestamp": "2026-02-08T06:08:02.412832Z"
} | ced808 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 1,
"correct": {
"strict": false,
"boxed": false,
"relaxed": true
},
"usage": {
"prompt_tokens": 249,
"completion_tokens": 940
},
"timestamp": "2026-02-18T23:45:25.574Z",
"answer": 7644
}
] | 0 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "ONE_PHI_2",
"status": "ok_later"
... | {
"lo": -6.48,
"mid": 1.54,
"hi": 9.56
} | ||
a48463 | alg_poly_orbit_hensel_v1_601307018_5112 | Let $N = a^3 - 4a \bmod 9409$ and $M = N^3 - 4N \bmod 9409$. Find the number of non-negative integers $a$ with $0 \le a \le 12212881$ such that $M = a$ and $N \ne a$. | 7,788 | graphs = [
Graph(
let={
"p1": Mod(value=Sum(Pow(Var("a"), Const(3)), Mul(Const(-4), Var("a"))), modulus=Const(9409)),
"p2": Mod(value=Sum(Pow(Ref("p1"), Const(3)), Mul(Const(-4), Ref("p1"))), modulus=Const(9409)),
"result": CountOverSet(set=SolutionsSet(var=Var("a"), cond... | ALG | null | COUNT | sympy | POLY_ORBIT_COUNT | [
"POLY_ORBIT_COUNT"
] | 4ad965 | alg_poly_orbit_hensel_v1 | null | 6 | null | [
"POLY_ORBIT_COUNT"
] | 1 | 0.048 | 2026-03-10T05:46:56.407884Z | {
"verified": true,
"answer": 7788,
"timestamp": "2026-03-10T05:46:56.456315Z"
} | 291727 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 183,
"completion_tokens": 5856
},
"timestamp": "2026-04-19T01:18:20.055Z",
"answer": 7788
},
{
"... | 1 | [
{
"lemma": "POLY_ORBIT_COUNT",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": 2.12,
"mid": 5.37,
"hi": 8.63
} | ||
cfcc71 | modular_inverse_v1_677425708_964 | Let $ a $ be the sum of all positive integers $ n $ such that $ 1 \leq n \leq 242 $ and $ n $ is divisible by 121. Let $ m = 1367 $. Let $ S $ be the set of all ordered pairs $ (x, y) $ of positive integers such that $ xy = 466489 $. Define $ \text{sum}(x, y) = x + y $, and let $ \text{upper} $ be the minimum value of ... | 51,750 | graphs = [
Graph(
let={
"a": SumOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Const(242)), Eq(Mod(value=Var("n"), modulus=Const(121)), Const(0))))),
"m": Const(1367),
"upper": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tup... | NT | null | EXTREMUM | sympy | SUM_DIVISIBLE | [
"SUM_DIVISIBLE",
"B3"
] | 26d1a5 | modular_inverse_v1 | null | 6 | 0 | [
"B3",
"SUM_DIVISIBLE"
] | 2 | 0.077 | 2026-02-08T03:53:50.429681Z | {
"verified": true,
"answer": 51750,
"timestamp": "2026-02-08T03:53:50.506778Z"
} | 33108c | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 328,
"completion_tokens": 1708
},
"timestamp": "2026-02-10T14:39:51.710Z",
"answer": 51750
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{... | {
"lo": -3.42,
"mid": 1.86,
"hi": 7.55
} | ||
b4ac4e | nt_sum_totient_over_divisors_v1_151522320_2308 | Let $n = 58964$. Define $\varphi(d)$ to be Euler's totient function. Compute
$$
\sum_{d \mid n} \varphi(d).
$$
Let this sum be $r$. Let $S$ be the set of all real numbers $x$ such that
$$
x^2 - 2x - 7055 = 0.
$$
Compute the value of
$$
\left( r^{\left| S \right|} + 9r + 7569 \right) \bmod 99773.
$$ | 2,945 | graphs = [
Graph(
let={
"_n": Const(99773),
"n": Const(58964),
"result": SumOverDivisors(n=Ref(name='n'), var='d', expr=EulerPhi(n=Var(name='d'))),
"Q": Mod(value=Sum(Pow(Ref("result"), SumOverSet(set=SolutionsSet(var=Var("x"), condition=Eq(Sum(Pow(Var("x"), C... | NT | null | COMPUTE | sympy | VIETA_SUM | [
"VIETA_SUM"
] | 833c91 | nt_sum_totient_over_divisors_v1 | quadratic_mod | 6 | 0 | [
"VIETA_SUM"
] | 1 | 0.002 | 2026-02-08T04:43:52.457724Z | {
"verified": true,
"answer": 2945,
"timestamp": "2026-02-08T04:43:52.459621Z"
} | 58063b | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 233,
"completion_tokens": 2457
},
"timestamp": "2026-02-11T21:48:59.219Z",
"answer": 2945
},
{
"... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
},
{
"lemma": "VIETA_SUM",
"status": "ok"
}
] | {
"lo": -3.42,
"mid": 1.86,
"hi": 7.55
} | ||
c08b01 | comb_binomial_compute_v1_1125832087_958 | Let $n = 14$. Define
$$
k = \sum_{k=1}^{3} \phi(k) \left\lfloor \frac{\sum_{k=1}^{2} k}{k} \right\rfloor,
$$
where $\phi$ denotes Euler's totient function. Compute $\binom{n}{k}$. | 3,003 | graphs = [
Graph(
let={
"_n": Const(2),
"n": Const(14),
"k": Summation(var="k", start=Const(1), end=Const(3), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(Summation(var="k", start=Const(1), end=Ref("_n"), expr=Var("k")), Var("k"))))),
"result": Binom(n=Ref("n"), k... | NT | null | COMPUTE | sympy | SUM_ARITHMETIC | [
"SUM_ARITHMETIC/K2"
] | 06cc86 | comb_binomial_compute_v1 | null | 5 | 0 | [
"K2",
"SUM_ARITHMETIC"
] | 2 | 0.001 | 2026-02-08T03:23:21.467485Z | {
"verified": true,
"answer": 3003,
"timestamp": "2026-02-08T03:23:21.468873Z"
} | db1d37 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 185,
"completion_tokens": 871
},
"timestamp": "2026-02-10T14:27:32.389Z",
"answer": 3003
},
{
"id... | 2 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K2",
"status": "ok_later"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "SUM_ARITH... | {
"lo": -10,
"mid": -7.73,
"hi": -5.46
} | ||
29a8c2 | sequence_count_fib_divisible_v1_784195855_3605 | Let $T$ be the set of all integers $t$ with $10 \le t \le 650$ for which there exist positive integers $a$ and $b$ such that $a \le 191$, $b \le 11$, and $t = 3a + 7b$. Let $u$ be the number of elements in $T$. Compute the number of positive integers $n$ with $1 \le n \le u$ such that the $n$th Fibonacci number is divi... | 89 | graphs = [
Graph(
let={
"upper": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=191)), Geq(left=Var(name='b'), right=Const(v... | NT | null | COUNT | sympy | COUNT_COPRIME_GRID | [
"LIN_FORM"
] | 7b2633 | sequence_count_fib_divisible_v1 | null | 7 | 0 | [
"COUNT_COPRIME_GRID",
"LIN_FORM"
] | 2 | 0.042 | 2026-02-08T06:32:35.549334Z | {
"verified": true,
"answer": 89,
"timestamp": "2026-02-08T06:32:35.591005Z"
} | 022f4f | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 159,
"completion_tokens": 3262
},
"timestamp": "2026-02-13T01:53:11.264Z",
"answer": 89
},
{
... | 1 | [
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
9f7af0 | antilemma_k2_v1_677425708_2962 | Let $n = 366$. Compute the value of $$\sum_{k=1}^{n} \phi(k) \left\lfloor \frac{366}{k} \right\rfloor,$$ where $\phi(k)$ denotes Euler's totient function. | 67,161 | graphs = [
Graph(
let={
"_n": Const(366),
"x": Summation(var="k", start=Const(1), end=Ref("_n"), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(Const(366), Var("k"))))),
},
goal=Ref("x"),
)
] | NT | COMB | COMPUTE | sympy | K13 | [
"K2"
] | 6897ab | antilemma_k2_v1 | null | 4 | 0 | [
"K13",
"K2"
] | 2 | 0.002 | 2026-02-08T05:23:59.817328Z | {
"verified": true,
"answer": 67161,
"timestamp": "2026-02-08T05:23:59.819110Z"
} | 1d8868 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 99,
"completion_tokens": 1305
},
"timestamp": "2026-02-12T07:27:36.604Z",
"answer": 67161
},
{... | 1 | [
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
}
] | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
f2ef9a | nt_count_coprime_and_v1_1742523217_15 | Let $n$ be a positive integer such that $1 \leq n \leq 24451$, $\gcd(n, 7) = 1$, and $\gcd(n, 9) = 1$. Let $A$ be the number of such integers $n$.
Let $S$ be the set of all ordered pairs $(x, y)$ of positive integers such that $x + y = 126$. Let $B$ be the maximum value of $xy$ over all such pairs.
Compute the remain... | 49,387 | graphs = [
Graph(
let={
"upper": Const(24451),
"k1": Const(7),
"k2": Const(9),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("upper")), Eq(GCD(a=Var("n"), b=Ref("k1")), Const(1)), Eq(GCD(a=Var("n... | NT | null | COUNT | sympy | B1 | [
"B1"
] | bf138c | nt_count_coprime_and_v1 | quadratic_mod | 5 | 0 | [
"B1"
] | 1 | 2.567 | 2026-02-08T02:50:24.931547Z | {
"verified": true,
"answer": 49387,
"timestamp": "2026-02-08T02:50:27.498284Z"
} | 6956c8 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 244,
"completion_tokens": 2637
},
"timestamp": "2026-02-08T19:57:37.572Z",
"answer": 49387
},
{
"... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no... | {
"lo": 2.21,
"mid": 3.69,
"hi": 5.22
} | ||
7d8de8 | nt_count_intersection_v1_1918700295_1734 | Let $a = \frac{3}{18} \sum_{k=1}^{2} \sum_{j=1}^{6} k$ and let $b = 22$. Compute the number of positive integers $n \leq 50000$ such that $a$ divides $n$ and $\gcd(n, b) = 1$. | 7,575 | graphs = [
Graph(
let={
"N": Const(50000),
"a": Div(Mul(Const(3), SumOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("k"), Var("_j")]), condition=Const(1), domain=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(2)), right=IntegerRange(start=Const(1), end=... | NT | null | COUNT | sympy | SUM_INDEPENDENT | [
"SUM_INDEPENDENT",
"SUM_ARITHMETIC"
] | 9f7183 | nt_count_intersection_v1 | null | 4 | 0 | [
"SUM_ARITHMETIC",
"SUM_INDEPENDENT"
] | 2 | 5.245 | 2026-02-08T05:58:32.927930Z | {
"verified": true,
"answer": 7575,
"timestamp": "2026-02-08T05:58:38.172430Z"
} | c68702 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 120,
"completion_tokens": 904
},
"timestamp": "2026-02-12T17:48:38.114Z",
"answer": 7575
},
{
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "SUM_ARITHMETIC",
"status": "ok... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
e08106 | lte_diff_endings_v1_1742523217_452 | Let $a = 27$ and $b = 11$. Compute $a - b$, and let $C$ be the largest integer $k$ such that $2^k$ divides $a - b$. Let $n = 63308$ and let $F = n!$. Let $D$ be the largest integer $k$ such that $2^k$ divides $F$. Define $T = n \cdot C + D$. Find the remainder when $T$ is divided by $100000$. | 16,530 | graphs = [
Graph(
let={
"a_val": Const(27),
"b_val": Const(11),
"p_val": Const(2),
"n_val": Const(63308),
"ab_diff": Sub(Ref("a_val"), Ref("b_val")),
"vp_ab": MaxKDivides(target=Ref("ab_diff"), base=Ref("p_val")),
"n_times_C... | NT | null | COMPUTE | sympy | LTE_DIFF | [
"LTE_DIFF"
] | cf8260 | lte_diff_endings_v1 | null | 4 | null | [
"LTE_DIFF"
] | 1 | 0 | 2026-02-08T03:03:25.248102Z | {
"verified": true,
"answer": 16530,
"timestamp": "2026-02-08T03:03:25.248569Z"
} | 316b93 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 223,
"completion_tokens": 1378
},
"timestamp": "2026-02-09T03:10:32.839Z",
"answer": 16530
},
{
... | 1 | [
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "ok"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
}
] | {
"lo": -6.49,
"mid": 0.51,
"hi": 7.52
} | ||
6f902d | lin_form_endings_v1_124444284_7732 | Let $a = 6$ and $b = 10$. Define $g = \gcd(a, b)$, $a' = \left\lfloor \frac{a}{g} \right\rfloor$, and $b' = \left\lfloor \frac{b}{g} \right\rfloor$. Let $A = 42$ and $B = 4$. Define
$$
T = a' \cdot A + b' \cdot B - a' \cdot b',
$$
and
$$
S = a \cdot A + b \cdot B - a - b + 1.
$$
Let $d = S - T$. Compute the remainder w... | 80,574 | graphs = [
Graph(
let={
"a_coeff": Const(6),
"b_coeff": Const(10),
"A_val": Const(42),
"B_val": Const(4),
"g_step": GCD(a=Ref("a_coeff"), b=Ref("b_coeff")),
"ap_node": Floor(Div(Ref("a_coeff"), Ref("g_step"))),
"bp_node": Fl... | COMB | NT | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | lin_form_endings_v1 | null | 5 | null | [
"LIN_FORM"
] | 1 | 0.001 | 2026-02-08T09:20:14.498534Z | {
"verified": true,
"answer": 80574,
"timestamp": "2026-02-08T09:20:14.499726Z"
} | 73f9a2 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 197,
"completion_tokens": 899
},
"timestamp": "2026-02-14T02:56:40.136Z",
"answer": 80574
},
{... | 1 | [
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"s... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
32e071 | nt_count_coprime_v1_458359167_5168 | Let $ k $ be the smallest divisor of 1225 that is at least 2. Determine the number of positive integers $ n $ such that $ 1 \leq n \leq 18225 $ and $ \gcd(n, k) = 1 $. Compute this number. | 14,580 | graphs = [
Graph(
let={
"upper": Const(18225),
"k": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(2)), Divides(divisor=Var("d"), dividend=Const(1225))))),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const... | NT | null | COUNT | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR"
] | bc3776 | nt_count_coprime_v1 | null | 3 | 0 | [
"MIN_PRIME_FACTOR"
] | 1 | 3.166 | 2026-02-08T12:19:05.642029Z | {
"verified": true,
"answer": 14580,
"timestamp": "2026-02-08T12:19:08.807727Z"
} | aa7dba | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 105,
"completion_tokens": 652
},
"timestamp": "2026-02-15T00:00:55.725Z",
"answer": 14580
},
{... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V7",
... | {
"lo": -9.12,
"mid": -6.02,
"hi": -3.62
} | ||
0b76e1 | antilemma_k3_v1_1918700295_1605 | Let $x = \sum_{d \mid 90935} \phi(d)$, where $\phi$ denotes Euler's totient function. Let $c$ be the sum of all real solutions $t$ to the equation $t^2 - 512t + 21436 = 0$. Compute the value of $(x^2 + 40x + c) \bmod 70977$. | 16,925 | graphs = [
Graph(
let={
"_m": Const(2),
"_n": Const(90935),
"x": SumOverDivisors(n=Ref(name='_n'), var='d', expr=EulerPhi(n=Var(name='d'))),
"_c": SumOverSet(set=SolutionsSet(var=Var("x"), condition=Eq(Sum(Pow(Var("x"), Const(2)), Mul(Const(-512), Var("x")), C... | NT | COMB | COMPUTE | sympy | VIETA_SUM | [
"VIETA_SUM",
"K3"
] | 74525f | antilemma_k3_v1 | quadratic_mod | 4 | 0 | [
"K3",
"VIETA_SUM"
] | 2 | 0.004 | 2026-02-08T05:54:28.870462Z | {
"verified": true,
"answer": 16925,
"timestamp": "2026-02-08T05:54:28.874815Z"
} | d98aa2 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 130,
"completion_tokens": 1446
},
"timestamp": "2026-02-12T17:11:00.471Z",
"answer": 16925
},
... | 1 | [
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
bf699c | nt_count_divisible_and_v1_349078426_957 | Let $d_1 = 6$ and $d_2 = \sum_{k=1}^{4} k$. Determine the number of positive integers $n$ such that $1 \leq n \leq 142590$, $n$ is divisible by $d_1$, and $n$ is divisible by $d_2$. Let this number be $r$. Let $s$ be the number of ordered pairs $(i,j)$ of positive integers with $1 \leq i \leq 82$, $1 \leq j \leq 153$, ... | 27,569 | graphs = [
Graph(
let={
"_n": Const(75764),
"upper": Const(142590),
"d1": Const(6),
"d2": Summation(var="k", start=Const(1), end=Const(4), expr=Var("k")),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), ... | NT | null | COUNT | sympy | COUNT_COPRIME_GRID | [
"COUNT_COPRIME_GRID",
"SUM_ARITHMETIC"
] | 83f63a | nt_count_divisible_and_v1 | affine_mod | 5 | 0 | [
"COUNT_COPRIME_GRID",
"SUM_ARITHMETIC"
] | 2 | 6.773 | 2026-02-08T13:20:52.483657Z | {
"verified": true,
"answer": 27569,
"timestamp": "2026-02-08T13:20:59.256896Z"
} | a9cca2 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 190,
"completion_tokens": 5759
},
"timestamp": "2026-02-15T13:28:56.281Z",
"answer": 27569
},
... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "ok"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
}... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
548231 | comb_count_permutations_fixed_v1_1440796553_1104 | Let $n$ be the number of positive integers $p$ for which there exists a positive integer $q$ such that $p < q$, $\gcd(p, q) = 1$, and $p \cdot q = 2315250$. Let $k = 6$. Define $r = \binom{n}{k} \cdot !(n - k)$, where $!(n - k)$ denotes the number of derangements of $n - k$ elements. Compute the remainder when $38917 \... | 2,611 | graphs = [
Graph(
let={
"n": CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Var(name='p')), Exists(var=Var(name='q'), condition=And(Eq(left=Mul(Var(name='p'), Var(name='q')), right=Const(value=2315250)), Eq(left=GCD(a=Var(name='p'), b=Var(name='q')), right=Const(value=1... | NT | COMB | COUNT | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS"
] | 2bb3aa | comb_count_permutations_fixed_v1 | null | 4 | 0 | [
"COPRIME_PAIRS"
] | 1 | 0.002 | 2026-02-08T12:11:31.206088Z | {
"verified": true,
"answer": 2611,
"timestamp": "2026-02-08T12:11:31.207787Z"
} | 1dd949 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 163,
"completion_tokens": 2159
},
"timestamp": "2026-02-14T22:55:05.222Z",
"answer": 2611
},
{... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
e9021e | nt_min_coprime_above_v1_677425708_1716 | Let $n = 50625$. Consider the set of all ordered pairs $(x, y)$ of positive integers such that $xy = 705600$. Let $s$ be the minimum value of $x + y$ over all such pairs. Let $m$ be the sum of all integer solutions $x$ to the equation $x^2 - 44x - 4700 = 0$. Let $r$ be the smallest integer $n$ such that $s < n \leq 173... | 48,944 | graphs = [
Graph(
let={
"_n": Const(50625),
"start": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Const(705600)))), expr=Sum(Var("x"), Var("... | NT | null | EXTREMUM | sympy | VIETA_SUM | [
"VIETA_SUM",
"B3"
] | 018050 | nt_min_coprime_above_v1 | null | 7 | 0 | [
"B3",
"VIETA_SUM"
] | 2 | 0.009 | 2026-02-08T04:23:09.840319Z | {
"verified": true,
"answer": 48944,
"timestamp": "2026-02-08T04:23:09.849144Z"
} | 5a76f0 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 236,
"completion_tokens": 1299
},
"timestamp": "2026-02-09T23:47:40.925Z",
"answer": 48944
},
{
"... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": ... | {
"lo": -3.46,
"mid": 1.03,
"hi": 5.49
} | ||
bb20e6 | comb_count_partitions_v1_1439011603_725 | Let $S$ be the set of all positive integers $n_2$ such that $1 \leq n_2 \leq 309$, $3$ divides $n_2$, and $\gcd(n_2, 10) = 1$. Let $m$ be the number of elements in $S$. Let $n$ be the largest prime number satisfying $2 \leq n \leq m$. Compute the remainder when $11025 - p(n)$ is divided by 94670, where $p(n)$ denotes t... | 61,112 | graphs = [
Graph(
let={
"_n": Const(94670),
"n": MaxOverSet(set=SolutionsSet(var=Var("n1"), condition=And(Geq(Var("n1"), Const(2)), Leq(Var("n1"), CountOverSet(set=SolutionsSet(var=Var("n2"), condition=And(Geq(Var("n2"), Const(1)), Leq(Var("n2"), Const(309)), Divides(divisor=Const(3)... | NT | COMB | COUNT | sympy | C5 | [
"C5/MAX_PRIME_BELOW"
] | e03314 | comb_count_partitions_v1 | null | 5 | 0 | [
"C5",
"MAX_PRIME_BELOW"
] | 2 | 0.003 | 2026-02-08T15:41:13.890667Z | {
"verified": true,
"answer": 61112,
"timestamp": "2026-02-08T15:41:13.893832Z"
} | 01bd91 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 165,
"completion_tokens": 1085
},
"timestamp": "2026-02-16T11:05:45.602Z",
"answer": 61112
},
... | 1 | [
{
"lemma": "C5",
"status": "ok"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok_later"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"st... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
ef5e26 | nt_min_phi_inverse_v1_1520064083_260 | Let $r$ be the smallest positive integer $n$ such that $1 \le n \le 10$ and Euler's totient function $\varphi(n) = 2$. Let $c$ be the number of integers $t$ such that $21 \le t \le 3717$ and there exist positive integers $a \le 658$ and $b \le 346$ satisfying $t = 3a + 5b + 13$. Compute $r \cdot c$. | 11,067 | graphs = [
Graph(
let={
"upper": Const(10),
"k": Const(2),
"result": MinOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("upper")), Eq(EulerPhi(n=Var("n")), Ref("k"))))),
"_c": CountOverSet(set=SolutionsSet(var=Va... | NT | null | EXTREMUM | sympy | LIN_FORM | [
"LIN_FORM"
] | 3d6396 | nt_min_phi_inverse_v1 | affine_mod | 6 | 0 | [
"LIN_FORM"
] | 1 | 0.004 | 2026-02-08T03:09:04.123828Z | {
"verified": true,
"answer": 11067,
"timestamp": "2026-02-08T03:09:04.127828Z"
} | f07b15 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 217,
"completion_tokens": 4434
},
"timestamp": "2026-02-10T13:05:49.713Z",
"answer": 11079
},
{
... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
}
] | {
"lo": 1.96,
"mid": 5.23,
"hi": 8.52
} | ||
f5bcdb | geo_count_lattice_rect_v1_865884756_4929 | Let $a = 324$ and $b = 84$. Define the set of lattice points in the rectangle $[0, a] \times [0, b]$ as the set of all ordered pairs $(x, y)$ of integers such that $0 \leq x \leq a$ and $0 \leq y \leq b$. Let $R$ be the number of such lattice points. Compute the value of $28561 - R$. | 936 | graphs = [
Graph(
let={
"a": Const(324),
"b": Const(84),
"result": LatticePointsRect(a=Ref(name='a'), b=Ref(name='b')),
"_c": Const(28561),
"Q": Sub(Ref("_c"), Ref("result")),
},
goal=Ref("Q"),
)
] | GEOM | null | COUNT | sympy | [] | geo_count_lattice_rect_v1 | null | 3 | 0 | null | null | 0.001 | 2026-02-08T18:17:13.070427Z | {
"verified": true,
"answer": 936,
"timestamp": "2026-02-08T18:17:13.071589Z"
} | 6562a3 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 140,
"completion_tokens": 538
},
"timestamp": "2026-02-24T23:46:43.449Z",
"answer": 936
},
{
... | 2 | [] | {
"lo": -10,
"mid": -7.4,
"hi": -4.8
} | ||||
dd1b3d | comb_binomial_compute_v1_1470522791_660 | Let $s = \sum_{k=0}^{5} (-1)^k \binom{5}{k}$ and $e = \sum_{k=0}^{10} (-1)^k \binom{10}{k}$. Let $n$ be the sum of $e$ and the number of integers $t$ in the range $7 \leq t \leq 24$ for which there exist positive integers $a \leq 4$ and $b \leq 3$ such that $t = 3a + 4b$. Let $k = 6 + s$. Compute $\binom{n}{k}$. | 924 | graphs = [
Graph(
let={
"u1": Const(4),
"n2": Sum(Ref("u1"), Const(1)),
"s": Summation(var="k", start=Const(0), end=Ref("n2"), expr=Mul(Pow(Const(-1), Var("k")), Binom(n=Ref("n2"), k=Var("k")))),
"u": Const(9),
"n1": Sum(Ref("u"), Const(1)),
... | COMB | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM/BINOMIAL_ALTERNATING"
] | bebeab | comb_binomial_compute_v1 | null | 5 | 2 | [
"BINOMIAL_ALTERNATING",
"LIN_FORM"
] | 2 | 0.006 | 2026-02-08T13:10:25.281790Z | {
"verified": true,
"answer": 924,
"timestamp": "2026-02-08T13:10:25.287305Z"
} | 3b0382 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 250,
"completion_tokens": 969
},
"timestamp": "2026-02-24T17:23:10.511Z",
"answer": 924
},
{
"id"... | 1 | [
{
"lemma": "BINOMIAL_ALTERNATING",
"status": "ok_later"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8... | {
"lo": -3.84,
"mid": -1.67,
"hi": 1.32
} | ||
3772bb | diophantine_fbi2_min_v1_655260480_1261 | Let $n = 2$ and $k = 16$. Let $d_0$ be the smallest integer $d$ such that $2 \leq d \leq 26$, $d$ divides $16$, and $\frac{16}{d} \geq 6$. Let $c$ be the minimum value of $x + y$ over all positive integers $x$ and $y$ such that $xy = 5345344$. Compute $c - d_0$. | 4,622 | graphs = [
Graph(
let={
"_n": Const(2),
"k": Const(16),
"upper": Const(26),
"result": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Ref("_n")), Leq(Var("d"), Ref("upper")), Divides(divisor=Var("d"), dividend=Ref("k")), Geq(Div(Ref("k"),... | NT | null | EXTREMUM | sympy | B3 | [
"B3"
] | fc629c | diophantine_fbi2_min_v1 | negation_mod | 4 | 0 | [
"B3"
] | 1 | 0.008 | 2026-02-08T16:00:45.770977Z | {
"verified": true,
"answer": 4622,
"timestamp": "2026-02-08T16:00:45.779000Z"
} | 969603 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 149,
"completion_tokens": 1123
},
"timestamp": "2026-02-16T19:17:25.621Z",
"answer": 4622
},
{... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
5cfd5c | antilemma_cartesian_v1_1978505735_4776 | Let $x$ be the number of ordered pairs $(i, j)$ such that $1 \leq i \leq 30$ and $1 \leq j \leq 45$. Let $Q$ be the remainder when $95509 \cdot x$ is divided by $71048$. Compute $Q$. | 56,078 | graphs = [
Graph(
let={
"x": CountOverSet(set=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(30)), right=IntegerRange(start=Const(1), end=Const(45)))),
"Q": Mod(value=Mul(Const(95509), Ref("x")), modulus=Const(71048)),
},
goal=Ref("Q"),
)
] | COMB | GEOM | COMPUTE | sympy | COUNT_CARTESIAN | [
"COUNT_CARTESIAN"
] | 409d7d | antilemma_cartesian_v1 | null | 2 | 0 | [
"COUNT_CARTESIAN"
] | 1 | 0.001 | 2026-02-08T18:30:28.190348Z | {
"verified": true,
"answer": 56078,
"timestamp": "2026-02-08T18:30:28.191450Z"
} | 41e8a7 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 111,
"completion_tokens": 1173
},
"timestamp": "2026-02-25T00:07:03.711Z",
"answer": 56078
},
... | 1 | [
{
"lemma": "COUNT_CARTESIAN",
"status": "ok"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status"... | {
"lo": -3.12,
"mid": 1.47,
"hi": 6.57
} | ||
01abf8 | antilemma_v7_kummer_168721529_808 | Determine the largest integer $x$ such that $2^x$ divides $\binom{395}{158}$. | 6 | graphs = [
Graph(
let={
"_n": Const(2),
"x": MaxKDivides(target=Binom(n=Const(395), k=Const(158)), base=Ref("_n")),
},
goal=Ref("x"),
)
] | NT | null | COMPUTE | sympy | C3 | [
"V7"
] | 0672d4 | antilemma_v7_kummer | null | 6 | 0 | [
"C3",
"V7"
] | 2 | 0.055 | 2026-02-08T13:18:19.102430Z | {
"verified": true,
"answer": 6,
"timestamp": "2026-02-08T13:18:19.157439Z"
} | 8db5f8 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 138,
"completion_tokens": 3137
},
"timestamp": "2026-02-09T09:26:43.877Z",
"answer": 6
},
{
"id":... | 1 | [
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "V7",
"status": "ok"
},
{
"lemma": "V8_SUM",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -6.69,
"mid": -2.39,
"hi": 1.83
} | ||
b600c4 | nt_min_coprime_above_v1_1520064083_3957 | Let $m$ be the largest prime number $n$ such that $2 \leq n \leq 461$. Compute the smallest integer $n$ greater than $18225$ and less than or equal to $18696$ such that $\gcd(n, m) = \sum_{d \mid \gcd(9,14)} \mu(d)$, where $\mu$ denotes the M\"obius function. Determine the value of this integer $n$. | 18,226 | graphs = [
Graph(
let={
"start": Const(18225),
"upper": Const(18696),
"modulus": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), Const(461)), IsPrime(Var("n"))))),
"result": MinOverSet(set=SolutionsSet(var=Var("n"... | NT | null | EXTREMUM | sympy | MOBIUS_COPRIME | [
"MOBIUS_COPRIME",
"MAX_PRIME_BELOW"
] | f86db3 | nt_min_coprime_above_v1 | null | 5 | 0 | [
"MAX_PRIME_BELOW",
"MOBIUS_COPRIME"
] | 2 | 0.08 | 2026-02-08T05:59:32.800248Z | {
"verified": true,
"answer": 18226,
"timestamp": "2026-02-08T05:59:32.880349Z"
} | 7b6e6d | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 200,
"completion_tokens": 291
},
"timestamp": "2026-02-18T21:49:24.480Z",
"answer": 18226
}
] | 2 | [
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MOBIUS_COPRIME",
"status": "ok"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "MOD_SUB",
"stat... | {
"lo": -10,
"mid": -6.47,
"hi": -2.95
} | ||
5ffb1c | comb_count_permutations_fixed_v1_1874849503_562 | Let $S$ be the set of all nonnegative integers $j$ such that $0 \leq j \leq 33800$ and $\binom{33800}{j} \equiv 1 \pmod{t}$, where $t$ is the number of ordered pairs of positive integers $(p, q)$ satisfying $p \cdot q = 54$, $\gcd(p, q) = 1$, and $p < q$. Let $n = |S|$. Compute the number of derangements of $n$ element... | 14,833 | graphs = [
Graph(
let={
"_n": Const(33800),
"n": CountOverSet(set=SolutionsSet(var=Var("j"), condition=And(Geq(Var("j"), Const(0)), Leq(Var("j"), Ref("_n")), Eq(Mod(value=Binom(n=Const(33800), k=Var("j")), modulus=CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(a... | NT | COMB | COUNT | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS/V8"
] | 93b9b8 | comb_count_permutations_fixed_v1 | null | 7 | 0 | [
"COPRIME_PAIRS",
"V8"
] | 2 | 0.006 | 2026-02-08T13:11:05.663000Z | {
"verified": true,
"answer": 14833,
"timestamp": "2026-02-08T13:11:05.669394Z"
} | 4d47da | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 228,
"completion_tokens": 2607
},
"timestamp": "2026-02-09T18:30:05.076Z",
"answer": 14833
},
{
"... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{... | {
"lo": -5.15,
"mid": 0.12,
"hi": 6.12
} | ||
57ef5d | antilemma_sum_equals_v1_784195855_9875 | Compute the number of ordered pairs $(i, j)$ of integers such that $1 \leq i \leq 51$, $1 \leq j \leq 51$, and $i + j = 51$. | 50 | graphs = [
Graph(
let={
"x": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=Eq(Sum(Var("i"), Var("j")), Const(51)), domain=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(51)), right=IntegerRange(start=Const(1), end=Const(51))))),
},
... | COMB | GEOM | COMPUTE | sympy | COUNT_SUM_EQUALS | [
"COUNT_SUM_EQUALS"
] | 75ab0f | antilemma_sum_equals_v1 | null | 2 | 0 | [
"COUNT_SUM_EQUALS"
] | 1 | 0.063 | 2026-02-08T17:15:02.651105Z | {
"verified": true,
"answer": 50,
"timestamp": "2026-02-08T17:15:02.714180Z"
} | 48226a | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 91,
"completion_tokens": 801
},
"timestamp": "2026-02-24T22:31:10.194Z",
"answer": 50
},
{
... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"stat... | {
"lo": -8.52,
"mid": -5.43,
"hi": -3.2
} | ||
e0c075 | geo_count_lattice_triangle_v1_168721529_582 | Let $m$ be the number of positive integers $n$ with $1 \leq n \leq 2313$ such that $9$ divides $n$ and $\gcd(n, 14) = 1$. Define
$$
a = \left| 111 \cdot \min\left\{ n \in \mathbb{Z}_{>0} : \nu_{13}(n!) \geq 14 \right\} - 225 \cdot 17 \right|,
$$
and
$$
b = \gcd(169, 17) + \gcd(56, 94) + \gcd(225, 111).
$$
Compute the v... | 7,465 | graphs = [
Graph(
let={
"_c": Const(2),
"_m": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Const(2313)), Divides(divisor=Const(9), dividend=Var("n")), Eq(GCD(a=Var("n"), b=Const(14)), Const(1))))),
"_n": Const(17),
... | NT | null | COUNT | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR",
"C5/V5"
] | 9cd50e | geo_count_lattice_triangle_v1 | null | 6 | 0 | [
"C5",
"MIN_PRIME_FACTOR",
"V5"
] | 3 | 0.011 | 2026-02-08T13:08:45.063360Z | {
"verified": true,
"answer": 7465,
"timestamp": "2026-02-08T13:08:45.074146Z"
} | d7a085 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 279,
"completion_tokens": 2135
},
"timestamp": "2026-02-09T06:36:17.723Z",
"answer": 7465
},
{
"i... | 1 | [
{
"lemma": "C5",
"status": "ok"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
... | {
"lo": -1.99,
"mid": 2.14,
"hi": 6.33
} | ||
c3c85f | sequence_lucas_compute_v1_349078426_1891 | Let $n$ be the number of positive integers $k$ such that $1 \leq k \leq 54$ and $2$ divides the $k$-th Fibonacci number. Compute the $n$-th Lucas number. | 5,778 | graphs = [
Graph(
let={
"_n": Const(2),
"n": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Const(54)), Divides(divisor=Ref("_n"), dividend=Fibonacci(arg=Var(name='n')))))),
"result": Lucas(arg=Ref(name='n')),
},
... | NT | null | COMPUTE | sympy | COUNT_FIB_DIVISIBLE | [
"COUNT_FIB_DIVISIBLE"
] | 66de3c | sequence_lucas_compute_v1 | null | 4 | 0 | [
"COUNT_FIB_DIVISIBLE"
] | 1 | 0.001 | 2026-02-08T13:59:02.430370Z | {
"verified": true,
"answer": 5778,
"timestamp": "2026-02-08T13:59:02.431593Z"
} | e74a2e | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 94,
"completion_tokens": 1049
},
"timestamp": "2026-02-15T22:45:34.151Z",
"answer": 5778
},
{
... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "ok"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
}
] | {
"lo": -5.49,
"mid": 0.22,
"hi": 6.51
} | ||
bfd807 | geo_count_lattice_triangle_v1_2051736721_2488 | Let $A$ be the area of a triangle with vertices at $(0,0)$, $(169,80)$, and $(40,128)$, multiplied by 2. Let $B$ be the sum of the greatest common divisors of the absolute differences of the coordinates of consecutive vertices, computed as follows:
- $\gcd(|169|, |80|)$,
- $\gcd(|40 - d|, |128 - 80|)$, where $d$ is th... | 9,211 | graphs = [
Graph(
let={
"_n": Const(40),
"area_2x": Abs(arg=Sum(Mul(Const(value=169), Const(value=128)), Mul(Ref(name='_n'), Sub(left=Const(value=0), right=Const(value=80))))),
"boundary": Sum(GCD(a=Abs(arg=Const(value=169)), b=Abs(arg=Const(value=80))), GCD(a=Abs(arg=Sub... | NT | null | COUNT | sympy | MAX_DIVISOR | [
"MAX_DIVISOR"
] | 51757e | geo_count_lattice_triangle_v1 | null | 6 | 0 | [
"MAX_DIVISOR"
] | 1 | 0.009 | 2026-02-08T16:44:04.135614Z | {
"verified": true,
"answer": 9211,
"timestamp": "2026-02-08T16:44:04.144843Z"
} | 324b34 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 186,
"completion_tokens": 1145
},
"timestamp": "2026-02-17T10:33:46.930Z",
"answer": 9211
},
{... | 1 | [
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MAX_DIVISOR",
"status": "ok"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
6d38ab | nt_count_digit_sum_v1_1520064083_7858 | Let $n = 2$. Let $s$ be the smallest divisor of $38152661$ that is at least $n$. Let $N$ be the number of positive integers $k$ such that $1 \leq k \leq 11027$ and the sum of the decimal digits of $k$ is equal to $s$. Compute $N$. | 120 | graphs = [
Graph(
let={
"_n": Const(2),
"upper": Const(11027),
"target_sum": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Ref("_n")), Divides(divisor=Var("d"), dividend=Const(38152661))))),
"result": CountOverSet(set=SolutionsSet(var=V... | NT | null | COUNT | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR"
] | bc3776 | nt_count_digit_sum_v1 | null | 4 | 0 | [
"MIN_PRIME_FACTOR"
] | 1 | 0.391 | 2026-02-08T09:20:49.633035Z | {
"verified": true,
"answer": 120,
"timestamp": "2026-02-08T09:20:50.024030Z"
} | a89dbe | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 122,
"completion_tokens": 3560
},
"timestamp": "2026-02-14T03:13:45.561Z",
"answer": 120
},
{
... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "V3",
"status": "no"... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
25bfe9 | antilemma_count_primes_v1_1874849503_790 | Let $m = 989$. Determine the number of prime numbers $n$ such that $2 \leq n \leq p_{\text{max}}$, where $p_{\text{max}}$ is the largest prime number less than or equal to $m$. Compute this count. | 166 | graphs = [
Graph(
let={
"_m": Const(989),
"_n": Const(2),
"x": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Ref("_n")), Leq(Var("n"), MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), Ref("_m")), IsPr... | NT | null | COMPUTE | sympy | LIN_FORM | [
"MAX_PRIME_BELOW/COUNT_PRIMES",
"COUNT_PRIMES"
] | eb1fd0 | antilemma_count_primes_v1 | null | 4 | 0 | [
"COUNT_PRIMES",
"LIN_FORM",
"MAX_PRIME_BELOW"
] | 3 | 0.055 | 2026-02-08T13:18:48.486283Z | {
"verified": true,
"answer": 166,
"timestamp": "2026-02-08T13:18:48.541419Z"
} | 2c50a2 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 170,
"completion_tokens": 892
},
"timestamp": "2026-02-09T20:57:05.103Z",
"answer": 166
},
{
"id"... | 1 | [
{
"lemma": "COUNT_PRIMES",
"status": "ok"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
... | {
"lo": -6.5,
"mid": -0.2,
"hi": 6.11
} | ||
e1e025 | algebra_quadratic_discriminant_v1_601307018_9729 | Let $a$ be an integer with $0 \leq a \leq 9408$. Define $M = (a^3 + 3a) \bmod 9409$, $R = (M^3 + 3M) \bmod 9409$, $S = (R^3 + 3R) \bmod 9409$, and $T = (S^3 + 3S) \bmod 9409$. Let $D = 81 - \left|\{ a_1 : 0 \leq a_1 \leq 9408,\ T = a_1,\ a_1 \notin \{M, R, S\} \}\right| \cdot (-3)$. Compute $2 \cdot [D > 0] + [D = 0]$. | 2 | graphs = [
Graph(
let={
"_n": Const(3),
"a": Const(1),
"b": Const(9),
"c": Const(-3),
"D": Sub(Pow(Ref("b"), Const(2)), Mul(CountOverSet(set=SolutionsSet(var=Var("a1"), condition=And(Geq(Var("a1"), Const(0)), Leq(Var("a1"), Const(9408)), Eq(Ref("_p... | ALG | null | COMPUTE | sympy | SUM_ARITHMETIC | [
"POLY_ORBIT_HENSEL"
] | 53b6eb | algebra_quadratic_discriminant_v1 | null | 6 | 0 | [
"POLY_ORBIT_HENSEL",
"SUM_ARITHMETIC"
] | 2 | 0.022 | 2026-03-10T10:08:52.193121Z | {
"verified": true,
"answer": 2,
"timestamp": "2026-03-10T10:08:52.214948Z"
} | d06949 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 291,
"completion_tokens": 894
},
"timestamp": "2026-04-19T11:56:20.503Z",
"answer": 2
},
{
"id":... | 2 | [
{
"lemma": "POLY_ORBIT_HENSEL",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": -10,
"mid": -5.89,
"hi": -1.79
} | ||
4a2a5d | comb_count_permutations_fixed_v1_124444284_7238 | Let $S$ be the set of all ordered pairs $(x, y)$ of positive integers such that $xy = 25$. Let $n$ be the minimum value of $x + y$ as $(x, y)$ ranges over $S$. Let $k = 7$. Define $r = \binom{n}{k} \cdot !{(n - k)}$, where $!m$ denotes the number of derangements of $m$ elements. Compute the remainder when $41443 \cdot ... | 38,292 | graphs = [
Graph(
let={
"_n": Const(84684),
"n": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Const(25)))), expr=Sum(Var("x"), Var("y")))),
... | COMB | null | COUNT | sympy | MIN_PRIME_FACTOR | [
"B3"
] | 0cd20d | comb_count_permutations_fixed_v1 | null | 6 | 0 | [
"B3",
"MIN_PRIME_FACTOR"
] | 2 | 0.019 | 2026-02-08T08:57:48.861295Z | {
"verified": true,
"answer": 38292,
"timestamp": "2026-02-08T08:57:48.880663Z"
} | df0112 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 228,
"completion_tokens": 1523
},
"timestamp": "2026-02-24T10:09:47.459Z",
"answer": 38292
},
{
"... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -2.35,
"mid": 1.22,
"hi": 4.84
} | ||
79554b | sequence_lucas_compute_v1_2051736721_1482 | Let $n$ be the number of integers $t$ such that $5 \leq t \leq 28$ and there exist positive integers $a$ and $b$ with $1 \leq a \leq 8$, $1 \leq b \leq 4$, and $t = 2a + 3b$. Compute the $n$-th Lucas number.
The Lucas numbers are defined by $L_1 = 1$, $L_2 = 3$, and $L_k = L_{k-1} + L_{k-2}$ for $k \geq 3$. | 39,603 | graphs = [
Graph(
let={
"n": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=8)), Geq(left=Var(name='b'), right=Const(value=1... | NT | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | sequence_lucas_compute_v1 | null | 4 | 0 | [
"LIN_FORM"
] | 1 | 0.001 | 2026-02-08T16:04:05.188966Z | {
"verified": true,
"answer": 39603,
"timestamp": "2026-02-08T16:04:05.190389Z"
} | 306cf9 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 173,
"completion_tokens": 1602
},
"timestamp": "2026-02-16T20:42:29.987Z",
"answer": 39603
},
... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
70ae04 | nt_gcd_compute_v1_124444284_753 | Let $a = 298863$ and $b = 564519$. Let $d_0 = \gcd(a, b)$. Let $S$ be the set of all integers $x$ such that $x^2 - 143x + 822 = 0$. Let $T$ be the set of all integers $d \geq 2$ that divide the sum of all elements of $S$. Let $m$ be the smallest element of $T$. Compute the Bell number $B_{|d_0| \bmod m}$. | 21,147 | graphs = [
Graph(
let={
"_n": Const(2),
"a": Const(298863),
"b": Const(564519),
"result": GCD(a=Ref("a"), b=Ref("b")),
"Q": Bell(Mod(value=Abs(arg=Ref(name='result')), modulus=MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Re... | NT | COMB | COMPUTE | sympy | VIETA_SUM | [
"VIETA_SUM/MIN_PRIME_FACTOR"
] | 9b23cf | nt_gcd_compute_v1 | bell_mod | 6 | 0 | [
"MIN_PRIME_FACTOR",
"VIETA_SUM"
] | 2 | 0.002 | 2026-02-08T03:29:38.051596Z | {
"verified": true,
"answer": 21147,
"timestamp": "2026-02-08T03:29:38.053511Z"
} | a57d7f | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 229,
"completion_tokens": 893
},
"timestamp": "2026-02-09T21:32:33.081Z",
"answer": 21147
},
{
"i... | 1 | [
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok_later"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
... | {
"lo": -3.46,
"mid": 1.03,
"hi": 5.49
} | ||
3e4d89 | comb_catalan_compute_v1_717093673_686 | Let $n$ be the number of ordered pairs $(a, b)$ such that $1 \le a \le 2$ and $1 \le b \le 5$. Let $r = C_n$, where $C_n$ denotes the $n$-th Catalan number. Find the remainder when $44121 \cdot r$ is divided by $94922$. | 262 | graphs = [
Graph(
let={
"_n": Const(94922),
"n": CountOverSet(set=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(2)), right=IntegerRange(start=Const(1), end=Const(5)))),
"result": Catalan(Ref("n")),
"Q": Mod(value=Mul(Const(44121), Ref("result"))... | COMB | null | COMPUTE | sympy | COUNT_CARTESIAN | [
"COUNT_CARTESIAN"
] | 409d7d | comb_catalan_compute_v1 | null | 2 | 0 | [
"COUNT_CARTESIAN"
] | 1 | 0.002 | 2026-02-08T15:36:04.985337Z | {
"verified": true,
"answer": 262,
"timestamp": "2026-02-08T15:36:04.987276Z"
} | 5314b4 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 190,
"completion_tokens": 1059
},
"timestamp": "2026-02-24T18:14:54.610Z",
"answer": 262
},
{
"i... | 1 | [
{
"lemma": "COUNT_CARTESIAN",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
... | {
"lo": -2.4,
"mid": 1.57,
"hi": 5.75
} | ||
6d7e77 | nt_count_divisors_in_range_v1_1742523217_4560 | Let $a$ be the number of positive integers $n$ with $1 \leq n \leq 20$ such that $\gcd(n, 21) = 1$. Let $n = 10080$ and $b = 1008$. Define $\text{result}$ as the number of positive divisors $d$ of $n$ such that $a \leq d \leq b$. Compute $\text{result} + 2^{\text{result} \bmod 15} \bmod 90940$. | 309 | graphs = [
Graph(
let={
"_n": Const(15),
"n": Const(10080),
"a": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Const(20)), Eq(GCD(a=Var("n"), b=Const(21)), Const(1))))),
"b": Const(1008),
"result":... | NT | null | COUNT | sympy | C4 | [
"C4"
] | 08d162 | nt_count_divisors_in_range_v1 | null | 5 | 0 | [
"C4"
] | 1 | 0.041 | 2026-02-08T08:58:12.996301Z | {
"verified": true,
"answer": 309,
"timestamp": "2026-02-08T08:58:13.036805Z"
} | f308fe | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 157,
"completion_tokens": 2156
},
"timestamp": "2026-02-13T22:38:12.623Z",
"answer": 309
},
{
... | 1 | [
{
"lemma": "C4",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
8c9a9b | comb_binomial_compute_v1_601307018_5106 | Let $R$ be the number of ordered pairs $(a, b)$ of positive integers with $1 \le a, b \le 40$ such that
\[
1028ab^3 + 257b^4 + C a^3 b + 257a^4 + 1542a^2b^2 = 1053860625,
\]
where $C = \left|\{ (a_1, b_1) : 1 \le a_1, b_1 \le 40,\, -12a_1b_1 + 20b_1^2 + 41a_1^2 \le 33761 \}\right|$. Let $n$ be the smallest value of $x ... | 792 | graphs = [
Graph(
let={
"_c": Const(2),
"_m": Const(4),
"_n": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), Const(40)), Geq(Var("b"), Const(1)), Leq(Var("b"), Const(40)), Eq(Sum(Mul(Const(1028)... | COMB | null | COMPUTE | sympy | QF_PSD_COUNT_LEQ | [
"QF_PSD_COUNT_LEQ/POLY4_COUNT/B3"
] | 825536 | comb_binomial_compute_v1 | null | 7 | 0 | [
"B3",
"POLY4_COUNT",
"QF_PSD_COUNT_LEQ"
] | 3 | 0.009 | 2026-03-10T05:46:23.333174Z | {
"verified": true,
"answer": 792,
"timestamp": "2026-03-10T05:46:23.341723Z"
} | 5dcdf4 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 296,
"completion_tokens": 9039
},
"timestamp": "2026-04-19T01:18:12.063Z",
"answer": 792
},
{
"i... | 1 | [
{
"lemma": "B3",
"status": "ok_later"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "POLY4_COUNT",
"status": "ok_later"
},
{
"lemma":... | {
"lo": -3.31,
"mid": 1.32,
"hi": 5.87
} | ||
7a8756 | antilemma_sum_factor_cartesian_v1_151522320_1520 | Let $S$ be the set of all ordered pairs $(i,j)$ of positive integers such that $1 \leq i \leq 26$ and $1 \leq j \leq 11$. Let $x$ be the sum of $i \cdot j$ over all pairs $(i,j)$ in $S$. Compute the remainder when $33271 \cdot x$ is divided by $52071$. | 1,044 | graphs = [
Graph(
let={
"x": SumOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=Const(1), domain=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(26)), right=IntegerRange(start=Const(1), end=Const(11)))), expr=Mul(Var("i"), Var("j")))),
... | NT | null | COMPUTE | sympy | K14 | [
"SUM_FACTOR_CARTESIAN"
] | d9e436 | antilemma_sum_factor_cartesian_v1 | null | 3 | 0 | [
"K14",
"SUM_FACTOR_CARTESIAN"
] | 2 | 0.018 | 2026-02-08T04:04:37.216693Z | {
"verified": true,
"answer": 1044,
"timestamp": "2026-02-08T04:04:37.234434Z"
} | ea02c7 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 187,
"completion_tokens": 443
},
"timestamp": "2026-02-18T08:19:32.443Z",
"answer": 1
}
] | 0 | [
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "SUM_FACTOR_CARTESIAN",
"status": "ok"
},
{
"lemma": "V5",
"status": "no"
... | {
"lo": -6.48,
"mid": 1.54,
"hi": 9.56
} | ||
b57342 | diophantine_sum_product_min_v1_1470522791_737 | Let $n = 876$ and $S = 85$. Let $P$ be the largest positive divisor $d$ of $773508$ such that $1 \leq d \leq n$. Determine the smallest positive integer $x$ such that $1 \leq x \leq 84$ and $x(S - x) = P$. | 12 | graphs = [
Graph(
let={
"_n": Const(876),
"S": Const(85),
"P": MaxOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(1)), Leq(Var("d"), Ref("_n")), Divides(divisor=Var("d"), dividend=Const(773508))))),
"result": MinOverSet(set=SolutionsSe... | NT | null | EXTREMUM | sympy | MAX_DIVISOR | [
"MAX_DIVISOR"
] | 51757e | diophantine_sum_product_min_v1 | null | 6 | 0 | [
"MAX_DIVISOR"
] | 1 | 0.02 | 2026-02-08T13:12:51.404966Z | {
"verified": true,
"answer": 12,
"timestamp": "2026-02-08T13:12:51.425046Z"
} | 04388c | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 119,
"completion_tokens": 1742
},
"timestamp": "2026-02-15T10:33:38.669Z",
"answer": 12
},
{
... | 1 | [
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MAX_DIVISOR",
"status": "ok"
}
] | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
3f3a32 | nt_count_gcd_equals_v1_124444284_748 | Let $S$ be the set of all ordered pairs $(x,y)$ of positive integers such that $xy = 1156$. Define $A$ to be the minimum value of $x + y$ over all pairs in $S$. Let $T$ be the set of all ordered pairs $(x,y)$ of positive integers such that $xy = 7214596$. Define $B$ to be the minimum value of $x + y$ over all pairs in ... | 46,378 | graphs = [
Graph(
let={
"upper": Const(27720),
"k": MaxOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(1)), Leq(Var("d"), MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPosit... | NT | null | COUNT | sympy | B3 | [
"B3/MAX_DIVISOR"
] | 33b851 | nt_count_gcd_equals_v1 | null | 7 | 0 | [
"B3",
"MAX_DIVISOR"
] | 2 | 2.171 | 2026-02-08T03:29:30.916543Z | {
"verified": true,
"answer": 46378,
"timestamp": "2026-02-08T03:29:33.087708Z"
} | 82f1cb | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 285,
"completion_tokens": 7090
},
"timestamp": "2026-02-09T21:32:38.355Z",
"answer": 46378
},
{
"... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "MAX_DIVISOR",
"status": "ok_later"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
... | {
"lo": -3.46,
"mid": 1.03,
"hi": 5.49
} | ||
0418c8 | comb_count_surjections_v1_1520064083_7805 | Let $k$ be the number of ordered pairs $(i,j)$ of positive integers such that $i + j = 4$ and $1 \leq i, j \leq 4$. Let $n$ be the number of ordered pairs $(a,b)$ where $a$ and $b$ are each in $\{1, 2\}$. Define $S(n,k)$ to be the number of ways to partition a set of $n$ labeled elements into $k$ nonempty unlabeled sub... | 36 | graphs = [
Graph(
let={
"_n": Const(4),
"n": CountOverSet(set=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(2)), right=IntegerRange(start=Const(1), end=Const(2)))),
"k": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=Eq(Su... | COMB | null | COUNT | sympy | COUNT_SUM_EQUALS | [
"COUNT_SUM_EQUALS",
"COUNT_CARTESIAN"
] | e4fc6a | comb_count_surjections_v1 | null | 3 | 0 | [
"COUNT_CARTESIAN",
"COUNT_SUM_EQUALS"
] | 2 | 0.011 | 2026-02-08T09:18:46.827323Z | {
"verified": true,
"answer": 36,
"timestamp": "2026-02-08T09:18:46.837934Z"
} | d80260 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 230,
"completion_tokens": 729
},
"timestamp": "2026-02-24T11:07:02.003Z",
"answer": 36
},
{
"id":... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "ok"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "n... | {
"lo": -5.97,
"mid": -3.97,
"hi": -1.93
} | ||
ce9f04 | antilemma_product_of_sums_v1_124444284_332 | Let $S_1$ be the sum of all integers $j$ with $0 \leq j \leq 15$ such that $\binom{15}{j}$ is odd. Let $S_2 = \sum_{k=1}^{29} k$. Let $x = S_1 \cdot S_2$. Find the remainder when $44121 \cdot x$ is divided by $65986$. | 6,842 | graphs = [
Graph(
let={
"S1": SumOverSet(set=SolutionsSet(var=Var("j"), condition=And(Geq(Var("j"), Const(0)), Leq(Var("j"), Const(15)), Eq(Mod(value=Binom(n=Const(15), k=Var("j")), modulus=Const(2)), Const(1))))),
"S2": Summation(var="k", start=Const(1), end=Const(29), expr=Var("k")... | NT | COMB | COMPUTE | sympy | PRODUCT_OF_SUMS | [
"PRODUCT_OF_SUMS"
] | f2b2b0 | antilemma_product_of_sums_v1 | null | 4 | 0 | [
"PRODUCT_OF_SUMS"
] | 1 | 0.001 | 2026-02-08T03:13:12.137357Z | {
"verified": true,
"answer": 6842,
"timestamp": "2026-02-08T03:13:12.137933Z"
} | 309aac | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 201,
"completion_tokens": 2309
},
"timestamp": "2026-02-09T16:18:34.868Z",
"answer": 6842
},
{
"i... | 1 | [
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "PRODUCT_OF_SUMS",
"status": "ok"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -6.51,
"mid": -0.31,
"hi": 5.43
} | ||
b143a0 | diophantine_fbi2_count_v1_865884756_3264 | Let $A$ be the set of positive integers $k_1$ such that $1 \le k_1 \le 17280$ and $24$ divides $k_1$. Let $m$ be the number of elements in $A$. Let $k$ be the number of positive integers $j$ such that $1 \le j \le m$ and $j^4 \le 268738560000$. Let $B$ be the set of integers $d$ such that $3 \le d \le 122$, $d$ divides... | 63,989 | graphs = [
Graph(
let={
"_n": Const(2),
"k": CountOverSet(set=SolutionsSet(var=Var("j"), condition=And(Geq(Var("j"), Const(1)), Leq(Var("j"), CountOverSet(set=SolutionsSet(var=Var("k1"), condition=And(Geq(Var("k1"), Const(1)), Leq(Var("k1"), Const(17280)), Divides(divisor=Const(24), ... | NT | null | COUNT | sympy | C2 | [
"C2/C3"
] | fd2b95 | diophantine_fbi2_count_v1 | null | 6 | 0 | [
"C2",
"C3"
] | 2 | 0.022 | 2026-02-08T17:14:57.714901Z | {
"verified": true,
"answer": 63989,
"timestamp": "2026-02-08T17:14:57.736460Z"
} | 215f24 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 202,
"completion_tokens": 1494
},
"timestamp": "2026-02-17T22:16:58.584Z",
"answer": 63989
},
... | 1 | [
{
"lemma": "C2",
"status": "ok"
},
{
"lemma": "C3",
"status": "ok_later"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
6723ea | modular_min_modexp_v1_1915831931_948 | Let $a = 7$, $b = 149$, and $m = 293$. Let $\text{upper}$ be the number of integers $t$ such that $32 \leq t \leq 347$ and there exist positive integers $a$ and $b$ with $1 \leq a \leq 57$, $1 \leq b \leq 6$, and $t = 5a + 7b + 20$.
Let $\text{result}$ be the smallest positive integer $x$ such that $1 \leq x \leq \tex... | 60,496 | graphs = [
Graph(
let={
"a": Const(7),
"b": Const(149),
"m": Const(293),
"upper": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), L... | NT | null | EXTREMUM | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | modular_min_modexp_v1 | null | 7 | 0 | [
"LIN_FORM"
] | 1 | 0.022 | 2026-02-08T15:46:05.147866Z | {
"verified": true,
"answer": 60496,
"timestamp": "2026-02-08T15:46:05.169846Z"
} | d3dbf0 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 212,
"completion_tokens": 3701
},
"timestamp": "2026-02-16T12:27:42.777Z",
"answer": 60496
},
... | 1 | [
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
8c162b | alg_telescope_v1_601307018_6557 | Find the remainder when $\sum_{k=0}^{D} \left((k + 1)^2 - k^2\right)$ is divided by $T$, where $D = \max \{ d \geq 1 : d \mid 3863134 \text{ and } d^2 \leq 3863134 \}$ and $T = \left|\{ t : \text{there exist integers } a, b \text{ with } 1 \leq a \leq 319,\ 1 \leq b \leq 1546 \text{ such that } t = 7a + 3b,\ 10 \leq t ... | 1,681 | graphs = [
Graph(
let={
"_n": Const(2),
"result": Mod(value=Summation(var="k", start=Const(0), end=MaxOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(1)), Divides(divisor=Var("d"), dividend=Const(3863134)), Leq(Mul(Var("d"), Var("d")), Const(3863134))))), exp... | NT | null | COMPUTE | sympy | B3_CLOSEST | [
"B3_CLOSEST",
"LIN_FORM"
] | a4198c | alg_telescope_v1 | null | 6 | 0 | [
"B3_CLOSEST",
"LIN_FORM"
] | 2 | 0.143 | 2026-03-10T07:11:14.160092Z | {
"verified": true,
"answer": 1681,
"timestamp": "2026-03-10T07:11:14.303500Z"
} | f95282 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 266,
"completion_tokens": 7477
},
"timestamp": "2026-04-19T04:42:34.947Z",
"answer": 1681
},
{
"... | 1 | [
{
"lemma": "B3_CLOSEST",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
... | {
"lo": -5.34,
"mid": 1.1,
"hi": 7.53
} | ||
cfbeb2 | nt_min_coprime_above_v1_153355830_150 | Let $p = 17$ and $q = 83$. Define $n_1 = p^2(q + 1)$. Let $v = \mu(n_1)^2$, where $\mu$ denotes the Möbius function. Let $n = 35$ and define
$$
f = \sum_{d \mid n} \mu(d).
$$
Let $\text{start} = 42436$ and $\text{upper} = 42553 + v$. Consider the set of all integers $n$ such that $n > \text{start}$, $n \leq \text{upper... | 68,867 | graphs = [
Graph(
let={
"p": Const(17),
"q": Const(83),
"n1": Mul(Pow(Ref("p"), Const(2)), Sum(Ref("q"), Const(1))),
"v": Pow(MoebiusMu(n=Ref(name='n1')), Const(2)),
"n": Const(35),
"f": SumOverDivisors(n=Ref(name='n'), var='d', expr=Mo... | NT | null | EXTREMUM | sympy | MOBIUS_SQUAREFREE | [
"MOBIUS_SQUAREFREE",
"MOBIUS_SUM"
] | 60a6e7 | nt_min_coprime_above_v1 | null | 6 | 2 | [
"MOBIUS_SQUAREFREE",
"MOBIUS_SUM"
] | 2 | 0.012 | 2026-02-08T02:55:04.750873Z | {
"verified": true,
"answer": 68867,
"timestamp": "2026-02-08T02:55:04.763154Z"
} | 8b5a77 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 292,
"completion_tokens": 842
},
"timestamp": "2026-02-17T15:59:34.803Z",
"answer": 42
}
] | 0 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "MOBIUS_SQUAREFREE",
"status": "ok"
},
{
"lemma": "MOBIUS_SUM",
"status": "ok"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V5",
"statu... | {
"lo": -6.48,
"mid": 1.54,
"hi": 9.56
} | ||
9e596f | diophantine_product_count_v1_1520064083_4966 | Let $n = 14400$. Define $k$ to be the minimum value of $x + y$ over all ordered pairs $(x, y)$ of positive integers such that $xy = n$.
Let $u$ be the smallest divisor of $2211538729$ that is at least $2$. Compute the number of positive integers $x$ such that $1 \leq x \leq u$, $x$ divides $k$, and $\frac{k}{x} \leq u... | 8 | graphs = [
Graph(
let={
"_n": Const(14400),
"k": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Ref("_n")))), expr=Sum(Var("x"), Var("y")))),
... | NT | null | COUNT | sympy | COUNT_FIB_DIVISIBLE | [
"MIN_PRIME_FACTOR",
"B3"
] | 6c6c26 | diophantine_product_count_v1 | null | 6 | 0 | [
"B3",
"COUNT_FIB_DIVISIBLE",
"MIN_PRIME_FACTOR"
] | 3 | 0.204 | 2026-02-08T06:31:58.645484Z | {
"verified": true,
"answer": 8,
"timestamp": "2026-02-08T06:31:58.849920Z"
} | 02bd81 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 149,
"completion_tokens": 1628
},
"timestamp": "2026-02-13T01:05:18.505Z",
"answer": 8
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma":... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
6d99e3 | lin_form_endings_v1_1918700295_2980 | Let $n = 70$, $a = 70$, and $b = 28$. Define $k = \left\lfloor \frac{n}{\gcd(a,b)} \right\rfloor$. Compute the remainder when $15000 \cdot k$ is divided by $53752$. | 21,248 | graphs = [
Graph(
let={
"_n": Const(70),
"a_coeff": Const(70),
"b_coeff": Const(28),
"_inner_result": Floor(Div(Ref("_n"), GCD(a=Ref("a_coeff"), b=Ref("b_coeff")))),
"_scale_k": Const(15000),
"_scaled": Mul(Ref("_scale_k"), Ref("_inner_... | COMB | NT | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | lin_form_endings_v1 | null | 3 | null | [
"LIN_FORM"
] | 1 | 0.001 | 2026-02-08T08:20:36.013281Z | {
"verified": true,
"answer": 21248,
"timestamp": "2026-02-08T08:20:36.013861Z"
} | 53b3c5 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 129,
"completion_tokens": 242
},
"timestamp": "2026-02-15T20:00:55.399Z",
"answer": 21248
},
{
"id": 11,
... | 2 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -10,
"mid": -7.73,
"hi": -5.46
} | ||
e729b3 | antilemma_k3_v1_1978505735_956 | Let $x$ be the sum of $\phi(d)$ over all positive divisors $d$ of $60056$. Let $s = \sum_{d \mid 4} \phi(d)$. Compute the remainder when $s - x$ is divided by $64583$. | 4,531 | graphs = [
Graph(
let={
"_n": Const(4),
"x": SumOverDivisors(n=Const(value=60056), var='d', expr=EulerPhi(n=Var(name='d'))),
"Q": Mod(value=Sub(SumOverDivisors(n=Ref(name='_n'), var='d1', expr=EulerPhi(n=Var(name='d1'))), Ref("x")), modulus=Const(64583)),
},
... | NT | COMB | COMPUTE | sympy | K13 | [
"K3",
"K3"
] | afd97d | antilemma_k3_v1 | negation_mod | 3 | 0 | [
"K13",
"K3"
] | 2 | 0.003 | 2026-02-08T15:43:06.973046Z | {
"verified": true,
"answer": 4531,
"timestamp": "2026-02-08T15:43:06.975962Z"
} | e4840e | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 104,
"completion_tokens": 296
},
"timestamp": "2026-02-16T11:38:05.605Z",
"answer": 4531
},
{
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
d5f881 | modular_mod_compute_v1_784195855_9435 | Let $n$ be a positive integer. Define $m$ to be the largest prime number less than or equal to 1550. Compute the remainder when $-37$ is divided by $m$. | 1,512 | graphs = [
Graph(
let={
"_n": Const(1550),
"a": Const(-37),
"m": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), Ref("_n")), IsPrime(Var("n"))))),
"result": Mod(value=Ref("a"), modulus=Ref("m")),
},
... | NT | null | COMPUTE | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW"
] | dc3ad3 | modular_mod_compute_v1 | null | 2 | 0 | [
"MAX_PRIME_BELOW"
] | 1 | 0.003 | 2026-02-08T16:48:49.635580Z | {
"verified": true,
"answer": 1512,
"timestamp": "2026-02-08T16:48:49.638154Z"
} | 097f51 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 88,
"completion_tokens": 745
},
"timestamp": "2026-02-17T13:40:29.775Z",
"answer": 1512
},
{
... | 1 | [
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
8d2af5 | nt_lcm_compute_v1_1439011603_2525 | Compute the least common multiple of $517$ and $748$. | 35,156 | graphs = [
Graph(
let={
"a": Const(517),
"b": Const(748),
"result": LCM(a=Ref("a"), b=Ref("b")),
},
goal=Ref("result"),
)
] | NT | null | COMPUTE | sympy | K13 | [
"COUNT_FIB_DIVISIBLE"
] | 66de3c | nt_lcm_compute_v1 | null | 2 | 0 | [
"COUNT_FIB_DIVISIBLE",
"K13"
] | 2 | 0.007 | 2026-02-08T16:50:59.906596Z | {
"verified": true,
"answer": 35156,
"timestamp": "2026-02-08T16:50:59.913097Z"
} | cd8e7e | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 60,
"completion_tokens": 795
},
"timestamp": "2026-02-17T13:34:34.097Z",
"answer": 35156
},
{
... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "ok"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V5",
"statu... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
ca1065 | nt_count_intersection_v1_601307018_252 | Let $M$ be the largest positive integer $d$ such that $d^2 \le 394375$ and $d \mid 394375$. Let $S$ be the number of positive integers $n$ with $1 \le n \le 100000$ such that $\gcd(n, 6) = 1$ and $5 \mid n$. Find the remainder when $S^2 + 15S + M$ is divided by $87662$. | 17,223 | graphs = [
Graph(
let={
"_n": Const(2),
"N": Const(100000),
"a": Const(5),
"b": Const(6),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("N")), Divides(divisor=Ref("a"), dividend=Var("... | NT | null | COUNT | sympy | B3_CLOSEST | [
"B3_CLOSEST"
] | d8bbcd | nt_count_intersection_v1 | quadratic_mod | 4 | 0 | [
"B3_CLOSEST"
] | 1 | 0.013 | 2026-03-10T00:48:43.496197Z | {
"verified": true,
"answer": 17223,
"timestamp": "2026-03-10T00:48:43.508970Z"
} | ede55b | CC BY 4.0 | null | null | [
{
"lemma": "B3_CLOSEST",
"status": "ok"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
}
] | {
"lo": -10,
"mid": 0,
"hi": 10
} | ||
3f3f27 | geo_visible_lattice_v1_2051736721_747 | Let $n = 111$. A visible lattice point $(x, y)$ is a point in the first quadrant with integer coordinates such that $1 \leq x, y \leq n$ and $\gcd(x, y) = 1$. Let $r$ be the number of visible lattice points.
Let $Q = 12321 - r$.
Compute $Q$. | 4,746 | graphs = [
Graph(
let={
"n": Const(111),
"result": VisibleLatticePoints(n=Ref(name='n')),
"Q": Sub(Const(12321), Ref("result")),
},
goal=Ref("Q"),
)
] | GEOM | null | COUNT | sympy | [] | geo_visible_lattice_v1 | null | 4 | 0 | null | null | 0.354 | 2026-02-08T15:39:12.354591Z | {
"verified": true,
"answer": 4746,
"timestamp": "2026-02-08T15:39:12.708451Z"
} | bc97ce | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 190,
"completion_tokens": 6222
},
"timestamp": "2026-02-24T18:19:28.202Z",
"answer": 4746
},
{
"... | 1 | [] | {
"lo": 1.98,
"mid": 5.23,
"hi": 8.52
} | ||||
94d1a7 | diophantine_sum_product_min_v1_1520064083_1351 | Let $ S = 32 $ and $ P = 87 $. Find the smallest positive integer $ x $ such that $ 1 \leq x \leq 31 $ and $ x(S - x) = P $. Compute this value of $ x $. | 3 | graphs = [
Graph(
let={
"S": Const(32),
"P": Const(87),
"result": MinOverSet(set=SolutionsSet(var=Var("x"), condition=And(Geq(Var("x"), Const(1)), Leq(Var("x"), Const(31)), Eq(Mul(Var("x"), Sub(Ref("S"), Var("x"))), Ref("P"))))),
},
goal=Ref("result"),
... | NT | null | EXTREMUM | sympy | B3 | [
"B3"
] | 0cd20d | diophantine_sum_product_min_v1 | null | 3 | 0 | [
"B3"
] | 1 | 0.03 | 2026-02-08T03:55:34.984388Z | {
"verified": true,
"answer": 3,
"timestamp": "2026-02-08T03:55:35.014375Z"
} | 47b823 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 164,
"completion_tokens": 337
},
"timestamp": "2026-02-10T16:12:48.594Z",
"answer": 3
},
{
"id": ... | 2 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
}
] | {
"lo": -10,
"mid": -7.73,
"hi": -5.46
} | ||
ec32d6 | alg_qf_psd_orbit_v1_1218484723_2071 | Let $A = \left|\{ t : \exists\, a,b \in \mathbb{Z}^+\ \text{with}\ 1 \leq a \leq 58, 1 \leq b \leq 63,\ t = 10a + 14b + 13,\ 37 \leq t \leq 1475 \}\right|$ and $B = \left|\{ (a_1, b_1) : 1 \leq a_1, b_1 \leq 30,\ 10a_1^2 - 18a_1 b_1 + 25b_1^2 \leq 10553 \}\right|$. Find the number of ordered triples $(a,b,c)$ of positi... | 20 | graphs = [
Graph(
let={
"_m": Const(2),
"_n": Const(18),
"result": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b"), Var("c")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), Const(18)), Geq(Var("b"), Const(1)), Leq(Var("b"), Const(18)), Geq(Var... | ALG | null | COUNT | sympy | ONE_PHI_2 | [
"QF_PSD_COUNT_LEQ",
"LIN_FORM"
] | 74f7c5 | alg_qf_psd_orbit_v1 | null | 6 | 0 | [
"LIN_FORM",
"ONE_PHI_2",
"QF_PSD_COUNT_LEQ"
] | 3 | 2.563 | 2026-02-25T03:46:47.271706Z | {
"verified": true,
"answer": 20,
"timestamp": "2026-02-25T03:46:49.834935Z"
} | 819b04 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 338,
"completion_tokens": 32768
},
"timestamp": "2026-03-29T02:53:36.673Z",
"answer": null
},
{
... | 1 | [
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "QF_PSD_COUNT_LEQ",
"status": "ok"
}
] | {
"lo": 4.43,
"mid": 6.62,
"hi": 9.7
} | ||
c45709 | lin_form_endings_v1_168721529_2065 | Let $a = 30$ and $b = 105$. Let $d$ be the greatest common divisor of $a$ and $b$. Let $k = 19856$ and define $\text{scaled} = k \cdot d$. Let $M = 87337$ and $x = \text{scaled} \mod M$. Compute $x$. | 35,829 | graphs = [
Graph(
let={
"a_coeff": Const(30),
"b_coeff": Const(105),
"_inner_result": GCD(a=Ref("a_coeff"), b=Ref("b_coeff")),
"_scale_k": Const(19856),
"_scaled": Mul(Ref("_scale_k"), Ref("_inner_result")),
"_mod_M": Const(87337),
... | COMB | NT | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | lin_form_endings_v1 | null | 2 | null | [
"LIN_FORM"
] | 1 | 0.001 | 2026-02-08T14:04:29.085027Z | {
"verified": true,
"answer": 35829,
"timestamp": "2026-02-08T14:04:29.085616Z"
} | 27f88c | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 188,
"completion_tokens": 294
},
"timestamp": "2026-02-10T01:36:14.390Z",
"answer": 35829
},
{
"i... | 2 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"st... | {
"lo": -10,
"mid": -7.27,
"hi": -4.54
} | ||
c6aeff_n | alg_poly3_min_v1_1218484723_1660 | A robot moves on a grid where each step depends on parameters $a$ and $b$, each ranging from 1 to 130. The energy cost of its path is given by $63a^2b + 35b^3 - 28a^3 - 63ab^2$. The robot selects $a$ and $b$ to minimize energy. What is the remainder when the minimum possible energy is divided by $54219$? | 48,949 | ALG | null | COMPUTE | sympy | POLY_ORBIT_HENSEL | [
"SUM_ARITHMETIC",
"ONE_PHI_2",
"C2"
] | 4feeef | alg_poly3_min_v1 | null | 3 | null | [
"C2",
"ONE_PHI_2",
"POLY_ORBIT_HENSEL",
"SUM_ARITHMETIC"
] | 4 | 2.218 | 2026-02-25T03:21:49.094110Z | null | 53652b | c6aeff | narrative | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 203,
"completion_tokens": 6905
},
"timestamp": "2026-03-30T17:10:39.470Z",
"answer": 48949
},
{
"... | 1 | [
{
"lemma": "C2",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
... | {
"lo": -5.37,
"mid": 0.23,
"hi": 5.22
} | |
20ce4a | nt_sum_gcd_range_mod_v1_865884756_3990 | Let $N$ be the largest positive divisor of $12152171$ that is at most $3481$. Compute the sum $\sum_{n=1}^{N} \gcd(n, 60)$, and find the remainder when this sum is divided by $11551$. | 9,330 | graphs = [
Graph(
let={
"N": MaxOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(1)), Leq(Var("d"), Const(3481)), Divides(divisor=Var("d"), dividend=Const(12152171))))),
"k": Const(60),
"M": Const(11551),
"sum": Summation(var="n", start... | NT | null | COMPUTE | sympy | MAX_DIVISOR | [
"MAX_DIVISOR"
] | 51757e | nt_sum_gcd_range_mod_v1 | null | 4 | 0 | [
"MAX_DIVISOR"
] | 1 | 0.188 | 2026-02-08T17:41:16.028148Z | {
"verified": true,
"answer": 9330,
"timestamp": "2026-02-08T17:41:16.215794Z"
} | f2f8e3 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 103,
"completion_tokens": 2814
},
"timestamp": "2026-02-18T06:38:30.162Z",
"answer": 9330
},
{... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MAX_DIVISOR",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
191cac | antilemma_k3_v1_349078426_1916 | Let $n = 43903$. Define $x = \sum_{d \mid n} \phi(d)$, where the sum is taken over all positive divisors $d$ of $n$, and $\phi$ denotes Euler's totient function. Compute the remainder when $x^2 + 11x + 3136$ is divided by $80114$. | 16,068 | graphs = [
Graph(
let={
"_n": Const(43903),
"x": SumOverDivisors(n=Ref(name='_n'), var='d', expr=EulerPhi(n=Var(name='d'))),
"Q": Mod(value=Sum(Pow(Ref("x"), Const(2)), Mul(Const(11), Ref("x")), Const(3136)), modulus=Const(80114)),
},
goal=Ref("Q"),
)
... | NT | COMB | COMPUTE | sympy | K13 | [
"K3"
] | 54c41e | antilemma_k3_v1 | null | 3 | 0 | [
"K13",
"K3"
] | 2 | 0.002 | 2026-02-08T13:59:48.439984Z | {
"verified": true,
"answer": 16068,
"timestamp": "2026-02-08T13:59:48.442323Z"
} | a3c1a1 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 121,
"completion_tokens": 3299
},
"timestamp": "2026-02-15T22:47:42.591Z",
"answer": 16068
},
... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
}
] | {
"lo": -5.49,
"mid": 0.22,
"hi": 6.51
} | ||
29a11e | antilemma_v1_legendre_1248542787_166 | Let $m = 2$ and $n = 31965$. Let $p$ be the largest prime number $q$ such that $m \leq q \leq d_{\min}$, where $d_{\min}$ is the smallest divisor of $29645$ that is at least $2$. Let $x$ be the largest integer $k$ such that $p^k$ divides $n!$. Compute $57600 - x$. | 49,611 | graphs = [
Graph(
let={
"_m": Const(2),
"_n": Const(31965),
"x": MaxKDivides(target=Factorial(Ref("_n")), base=MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Ref("_m")), Leq(Var("n"), MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("... | NT | null | COMPUTE | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR/MAX_PRIME_BELOW/V1",
"V1"
] | 012ceb | antilemma_v1_legendre | null | 6 | 0 | [
"MAX_PRIME_BELOW",
"MIN_PRIME_FACTOR",
"V1"
] | 3 | 0.002 | 2026-02-08T02:58:57.662031Z | {
"verified": true,
"answer": 49611,
"timestamp": "2026-02-08T02:58:57.663975Z"
} | 8769e3 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 209,
"completion_tokens": 1184
},
"timestamp": "2026-02-09T01:00:30.535Z",
"answer": 49611
},
{
"... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K5",
"status": "same_pattern_wrong"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status... | {
"lo": -6.51,
"mid": -0.31,
"hi": 5.43
} | ||
9d2e04 | nt_count_primes_v1_124444284_8656 | Let $p$ and $q$ be positive integers such that $pq = 18$, $\gcd(p, q) = 1$, and $p < q$. Let $c$ be the number of such pairs $(p, q)$. Let $S$ be the set of all prime numbers $n$ such that $n \geq c$ and $n \leq 19044$. Let $r$ be the number of elements in $S$. Compute the remainder when $55151 \cdot r$ is divided by $... | 45,237 | graphs = [
Graph(
let={
"_n": Const(50808),
"upper": Const(19044),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Var(name='p')), Exists(var=Var(name='q'), conditio... | NT | null | COUNT | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS"
] | 2bb3aa | nt_count_primes_v1 | null | 4 | 0 | [
"COPRIME_PAIRS"
] | 1 | 0.453 | 2026-02-08T11:51:36.579805Z | {
"verified": true,
"answer": 45237,
"timestamp": "2026-02-08T11:51:37.033155Z"
} | e5e35e | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 159,
"completion_tokens": 3076
},
"timestamp": "2026-02-14T19:46:50.552Z",
"answer": 45237
},
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
ce3094 | nt_count_digit_sum_v1_1440796553_876 | Let $x$ and $y$ be positive integers such that $xy = 64$. Define $s$ to be the minimum possible value of $x + y$ over all such pairs. Let $N$ be the number of positive integers $n$ less than or equal to $16384$ such that the sum of the digits of $n$ is equal to $s$. Compute $N$. | 1,095 | graphs = [
Graph(
let={
"upper": Const(16384),
"target_sum": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Const(64)))), expr=Sum(Var("x"), V... | NT | null | COUNT | sympy | B3 | [
"B3"
] | 0cd20d | nt_count_digit_sum_v1 | null | 4 | 0 | [
"B3"
] | 1 | 1.212 | 2026-02-08T12:02:04.002688Z | {
"verified": true,
"answer": 1095,
"timestamp": "2026-02-08T12:02:05.215045Z"
} | f05a94 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 130,
"completion_tokens": 4413
},
"timestamp": "2026-02-14T21:54:34.531Z",
"answer": 1095
},
{... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
161664 | nt_count_divisors_in_range_v1_677425708_3606 | Let $a$ be the largest positive divisor of $1599$ that is at most $39$. Let $b$ be the minimum value of $x + y$ over all pairs of positive integers $(x, y)$ such that $xy = 1592644$. Compute the number of positive divisors $d$ of $15120$ such that $a \leq d \leq b$. | 52 | graphs = [
Graph(
let={
"_n": Const(39),
"n": Const(15120),
"a": MaxOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(1)), Leq(Var("d"), Ref("_n")), Divides(divisor=Var("d"), dividend=Const(1599))))),
"b": MinOverSet(set=MapOverSet(set=S... | NT | null | COUNT | sympy | SUM_INDEPENDENT | [
"MAX_DIVISOR",
"B3"
] | a4accf | nt_count_divisors_in_range_v1 | null | 6 | 0 | [
"B3",
"MAX_DIVISOR",
"SUM_INDEPENDENT"
] | 3 | 0.086 | 2026-02-08T05:51:30.419236Z | {
"verified": true,
"answer": 52,
"timestamp": "2026-02-08T05:51:30.504956Z"
} | eae11c | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 128,
"completion_tokens": 2880
},
"timestamp": "2026-02-12T15:17:08.365Z",
"answer": 52
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "MAX_DIVISOR",
"status": "... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
cd4f28 | geo_count_lattice_rect_v1_124444284_8706 | Compute the number of lattice points $(x, y)$ such that $0 \le x \le 400$ and $0 \le y \le 163$. | 65,764 | graphs = [
Graph(
let={
"a": Const(400),
"b": Const(163),
"result": LatticePointsRect(a=Ref(name='a'), b=Ref(name='b')),
},
goal=Ref("result"),
)
] | GEOM | null | COUNT | sympy | [] | geo_count_lattice_rect_v1 | null | 3 | 0 | null | null | 0.001 | 2026-02-08T11:52:31.509569Z | {
"verified": true,
"answer": 65764,
"timestamp": "2026-02-08T11:52:31.510937Z"
} | cfc943 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 144,
"completion_tokens": 163
},
"timestamp": "2026-02-24T14:57:11.887Z",
"answer": 65764
},
{
"i... | 1 | [] | {
"lo": -4.92,
"mid": -2.91,
"hi": -0.68
} | ||||
2d705e | comb_count_partitions_v1_124444284_6071 | Let $p$ be a positive integer. Define $n$ to be the smallest positive divisor of $3563023$ that is at least the number of such $p$ for which there exists a positive integer $q > p$ with $pq = 36$ and $\gcd(p, q) = 1$. Compute the number of integer partitions of $n$. | 44,583 | graphs = [
Graph(
let={
"_n": CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Var(name='p')), Exists(var=Var(name='q'), condition=And(Eq(left=Mul(Var(name='p'), Var(name='q')), right=Const(value=36)), Eq(left=GCD(a=Var(name='p'), b=Var(name='q')), right=Const(value=1)), ... | NT | COMB | COUNT | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS/MIN_PRIME_FACTOR"
] | 52cee2 | comb_count_partitions_v1 | null | 5 | 0 | [
"COPRIME_PAIRS",
"MIN_PRIME_FACTOR"
] | 2 | 0.003 | 2026-02-08T08:06:39.948725Z | {
"verified": true,
"answer": 44583,
"timestamp": "2026-02-08T08:06:39.951244Z"
} | a35af9 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 123,
"completion_tokens": 2861
},
"timestamp": "2026-02-13T14:43:52.479Z",
"answer": 44583
},
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status":... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
07b486 | nt_sum_gcd_range_mod_v1_1440796553_156 | Let $S$ be the set of all ordered pairs $(x, y)$ of positive integers such that $xy = 1669264$. Define $T$ as the set of all values $x + y$ where $(x, y) \in S$. Let $N$ be the minimum value in $T$. Let $k = 504$ and $M = 10009$. Compute the remainder when $$\sum_{n=1}^{N} \gcd(n, k)$$ is divided by $M$. | 7,822 | graphs = [
Graph(
let={
"N": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Const(1669264)))), expr=Sum(Var("x"), Var("y")))),
"k": Const(504)... | NT | null | COMPUTE | sympy | B3 | [
"B3"
] | 0cd20d | nt_sum_gcd_range_mod_v1 | null | 6 | 0 | [
"B3"
] | 1 | 0.228 | 2026-02-08T11:37:11.727012Z | {
"verified": true,
"answer": 7822,
"timestamp": "2026-02-08T11:37:11.955398Z"
} | 54610d | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 154,
"completion_tokens": 3363
},
"timestamp": "2026-02-14T16:48:14.088Z",
"answer": 7822
},
{... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
}
] | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
4bdab6 | sequence_lucas_compute_v1_1742523217_1239 | Let $n$ be the number of integers $t$ such that $27 \leq t \leq 102$ and there exist integers $a$ and $b$ with $1 \leq a \leq 10$, $1 \leq b \leq 2$, and $t = 6a + 21b$. Let $L_n$ denote the $n$-th Lucas number, defined by $L_1 = 1$, $L_2 = 3$, and $L_k = L_{k-1} + L_{k-2}$ for $k \geq 3$. Compute the remainder when $9... | 59,507 | graphs = [
Graph(
let={
"_n": Const(94351),
"n": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=10)), Geq(left=V... | NT | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | sequence_lucas_compute_v1 | null | 5 | 0 | [
"LIN_FORM"
] | 1 | 0.001 | 2026-02-08T03:34:41.348662Z | {
"verified": true,
"answer": 59507,
"timestamp": "2026-02-08T03:34:41.350148Z"
} | 1bfe86 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 264,
"completion_tokens": 1017
},
"timestamp": "2026-02-10T05:31:29.298Z",
"answer": 59507
},
{
"... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
}
] | {
"lo": -3.46,
"mid": 1.03,
"hi": 5.49
} | ||
02ef2c | modular_count_residue_v1_458359167_2011 | Let $m$ be the minimum value of $x + y$ over all ordered pairs $(x, y)$ of positive integers such that $xy = 25$. Let $N$ be the number of integers $n$ with $1 \leq n \leq 34969$ such that $n \equiv 0 \pmod{m}$. Compute the remainder when $24247 \cdot N$ is divided by $79264$. | 34,296 | graphs = [
Graph(
let={
"_n": Const(24247),
"upper": Const(34969),
"m": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Const(25)))... | NT | null | COUNT | sympy | B3 | [
"B3"
] | 0cd20d | modular_count_residue_v1 | null | 4 | 0 | [
"B3"
] | 1 | 1.134 | 2026-02-08T04:58:10.480664Z | {
"verified": true,
"answer": 34296,
"timestamp": "2026-02-08T04:58:11.614347Z"
} | 9f3d26 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 205,
"completion_tokens": 1306
},
"timestamp": "2026-02-11T22:33:02.027Z",
"answer": 34296
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -3.49,
"mid": 1.84,
"hi": 7.55
} | ||
05cb7d | algebra_quadratic_discriminant_v1_655260480_4648 | Let $a = -2$, $b = 4$, and $c = -2$. The discriminant $D$ of the quadratic equation $ax^2 + bx + c = 0$ is given by $D = b^2 - 4ac$. Define $\alpha = 1$ if $D > 0$, and $\alpha = 0$ otherwise. Define $\beta = 1$ if
$$
D = \sum_{k=0}^{6} (-1)^k \binom{6}{k},
$$
and $\beta = 0$ otherwise. Compute $2\alpha + \beta$. | 1 | graphs = [
Graph(
let={
"a": Const(-2),
"b": Const(4),
"c": Const(-2),
"D": Sub(Pow(Ref("b"), Const(2)), Mul(Const(4), Ref("a"), Ref("c"))),
"result": Sum(Mul(Const(2), Iverson(condition=Gt(Ref("D"), Const(0)))), Iverson(condition=Eq(Ref("D"), Summ... | COMB | null | COMPUTE | sympy | K14 | [
"BINOMIAL_ALTERNATING"
] | c21569 | algebra_quadratic_discriminant_v1 | null | 4 | 0 | [
"BINOMIAL_ALTERNATING",
"K14"
] | 2 | 0.053 | 2026-02-08T18:02:50.087587Z | {
"verified": true,
"answer": 1,
"timestamp": "2026-02-08T18:02:50.140685Z"
} | e0555f | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 175,
"completion_tokens": 520
},
"timestamp": "2026-02-24T23:17:52.534Z",
"answer": 1
},
{
... | 1 | [
{
"lemma": "BINOMIAL_ALTERNATING",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status":... | {
"lo": -6.4,
"mid": -4.13,
"hi": -2.01
} | ||
20a127 | modular_modexp_compute_v1_151522320_1127 | Let $e$ be the number of positive integers $n \leq 1864$ such that $21$ divides the $n$th Fibonacci number. Compute the remainder when $41^e$ is divided by $60025$. | 59,471 | graphs = [
Graph(
let={
"_n": Const(21),
"a": Const(41),
"e": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Const(1864)), Divides(divisor=Ref("_n"), dividend=Fibonacci(arg=Var(name='n')))))),
"m": Const(60025)... | NT | null | COMPUTE | sympy | COUNT_FIB_DIVISIBLE | [
"COUNT_FIB_DIVISIBLE"
] | 66de3c | modular_modexp_compute_v1 | null | 7 | 0 | [
"COUNT_FIB_DIVISIBLE"
] | 1 | 0.002 | 2026-02-08T03:48:56.650767Z | {
"verified": true,
"answer": 59471,
"timestamp": "2026-02-08T03:48:56.652461Z"
} | 974571 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 159,
"completion_tokens": 3550
},
"timestamp": "2026-02-10T15:49:52.122Z",
"answer": 59471
},
{
"... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "ok"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
}
... | {
"lo": -3.46,
"mid": 1.03,
"hi": 5.49
} | ||
769ad9 | comb_binomial_compute_v1_1915831931_403 | Let $n = 15$ and let $k$ be the smallest divisor of $143143$ that is at least $2$. Define $\mathrm{result} = \binom{n}{k}$. Compute the remainder when $44121 \cdot \mathrm{result}$ is divided by $85909$. | 75,299 | graphs = [
Graph(
let={
"_n": Const(2),
"n": Const(15),
"k": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Ref("_n")), Divides(divisor=Var("d"), dividend=Const(143143))))),
"result": Binom(n=Ref("n"), k=Ref("k")),
"Q": Mod(v... | NT | null | COMPUTE | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR"
] | bc3776 | comb_binomial_compute_v1 | null | 3 | 0 | [
"MIN_PRIME_FACTOR"
] | 1 | 0.002 | 2026-02-08T15:24:22.786323Z | {
"verified": true,
"answer": 75299,
"timestamp": "2026-02-08T15:24:22.788379Z"
} | 340617 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 109,
"completion_tokens": 1435
},
"timestamp": "2026-02-16T05:10:27.844Z",
"answer": 75299
},
... | 1 | [
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
ef6b8c | comb_count_permutations_fixed_v1_1820931509_386 | Let $m = 8$ and $n_0 = 44121$. Let $d$ be the smallest divisor of $537251$ that is at least $2$. Let $k$ be the number of positive integers $n$ with $1 \leq n \leq 48$ such that $m$ divides $F_n$, where $F_n$ denotes the $n$th Fibonacci number. Compute $\binom{d}{k} \cdot !\!(d - k)$, where $!\!n$ denotes the number of... | 27,120 | graphs = [
Graph(
let={
"_m": Const(8),
"_n": Const(44121),
"n": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(2)), Divides(divisor=Var("d"), dividend=Const(537251))))),
"k": CountOverSet(set=SolutionsSet(var=Var("n"), condition=A... | NT | COMB | COUNT | sympy | COUNT_FIB_DIVISIBLE | [
"COUNT_FIB_DIVISIBLE",
"MIN_PRIME_FACTOR"
] | d4f327 | comb_count_permutations_fixed_v1 | null | 6 | 0 | [
"COUNT_FIB_DIVISIBLE",
"MIN_PRIME_FACTOR"
] | 2 | 0.003 | 2026-02-08T11:34:39.061496Z | {
"verified": true,
"answer": 27120,
"timestamp": "2026-02-08T11:34:39.064016Z"
} | dfb28c | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 196,
"completion_tokens": 1802
},
"timestamp": "2026-02-14T15:59:07.509Z",
"answer": 27120
},
... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "ok"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V8",
"status": "n... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
85028a | diophantine_fbi2_min_v1_397696148_2466 | Let $n = 9025$. Consider the set of all ordered pairs $(x, y)$ of positive integers such that $xy = n$. Define $s$ to be the minimum value of $x + y$ over all such pairs.
Now let $k = 180$. Find the smallest divisor $d$ of $k$ such that $d \geq 2$, $d \leq s$, and $\frac{k}{d} \geq 4$.
Compute the value of this divis... | 2 | graphs = [
Graph(
let={
"_n": Const(9025),
"k": Const(180),
"upper": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Ref("_n")))), ... | NT | null | EXTREMUM | sympy | COPRIME_PAIRS | [
"B3"
] | 0cd20d | diophantine_fbi2_min_v1 | null | 4 | 0 | [
"B3",
"COPRIME_PAIRS"
] | 2 | 0.045 | 2026-02-08T13:20:19.612106Z | {
"verified": true,
"answer": 2,
"timestamp": "2026-02-08T13:20:19.657583Z"
} | 281af9 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 152,
"completion_tokens": 965
},
"timestamp": "2026-02-15T14:34:05.192Z",
"answer": 2
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
}
] | {
"lo": -5.49,
"mid": 0.22,
"hi": 6.51
} | ||
7266a1 | diophantine_fbi2_count_v1_1915831931_3214 | Let $S$ be the set of all ordered pairs $(x, y)$ of positive integers such that $xy = 396900$. Define $T$ to be the set of all values $x + y$ where $(x, y) \in S$. Let $k$ be the minimum value in $T$. Let $U$ be the set of all ordered pairs $(x_1, y_1)$ of positive integers such that $x_1 y_1 = 2704$. Define $V$ to be ... | 52 | graphs = [
Graph(
let={
"_m": Const(6),
"_n": Const(5),
"k": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Const(396900)))), expr... | NT | null | COUNT | sympy | B3 | [
"B3"
] | 0cd20d | diophantine_fbi2_count_v1 | null | 6 | 0 | [
"B3"
] | 1 | 0.024 | 2026-02-08T17:25:40.168526Z | {
"verified": true,
"answer": 52,
"timestamp": "2026-02-08T17:25:40.192821Z"
} | 5e2034 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 285,
"completion_tokens": 2041
},
"timestamp": "2026-02-18T02:53:32.695Z",
"answer": 52
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
5cdacd | nt_sum_divisors_compute_v1_1918700295_1783 | Let $n = 29241$. Compute the sum of all positive divisors of $n$. | 46,101 | graphs = [
Graph(
let={
"n": Const(29241),
"result": SumDivisors(n=Ref("n")),
},
goal=Ref("result"),
)
] | NT | null | COMPUTE | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS/DIVISOR_PARITY",
"WILSON"
] | cb6605 | nt_sum_divisors_compute_v1 | null | 2 | 0 | [
"COPRIME_PAIRS",
"DIVISOR_PARITY",
"WILSON"
] | 3 | 0.007 | 2026-02-08T06:01:24.355219Z | {
"verified": true,
"answer": 46101,
"timestamp": "2026-02-08T06:01:24.361880Z"
} | 4fd8f3 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 66,
"completion_tokens": 702
},
"timestamp": "2026-02-12T17:50:48.762Z",
"answer": 46101
},
{
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "DIVISOR_PARITY",
"status": "ok_later"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
d9aaf7 | antilemma_k2_v1_655260480_4747 | Let
$$
x = \sum_{k=1}^{300} \phi(k) \left\lfloor \frac{300}{k} \right\rfloor.
$$
Let $c$ be the sum of $\phi(d)$ over all positive divisors $d$ of $7001$. Let $m = 313$, and let $s$ be the sum of $\phi(d)$ over all positive divisors $d$ of $m$. Compute the remainder when $\left( x \bmod 317 \right) + c \cdot \left( x \... | 33,144 | graphs = [
Graph(
let={
"_m": Const(313),
"_n": Const(51307),
"x": Summation(var="k", start=Const(1), end=Const(300), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(Const(300), Var("k"))))),
"_c": SumOverDivisors(n=Const(value=7001), var='d', expr=EulerPhi(n=Var(nam... | NT | COMB | COMPUTE | sympy | K13 | [
"K3",
"K2"
] | da970e | antilemma_k2_v1 | two_moduli | 6 | 0 | [
"K13",
"K2",
"K3"
] | 3 | 0.006 | 2026-02-08T18:06:06.231618Z | {
"verified": true,
"answer": 33144,
"timestamp": "2026-02-08T18:06:06.237514Z"
} | aac257 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 175,
"completion_tokens": 2939
},
"timestamp": "2026-02-18T14:02:58.895Z",
"answer": 33144
},
... | 1 | [
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": ... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
6d4725 | alg_linear_system_2x2_v1_601307018_1494 | Let $\text{det} = (-19)(-11) - (-19)\sum_{k=0}^{2} 2^k$, $R = (-74810)(-11) - (-79580)\cdot\min\{d : d \geq 2, d \mid 11011\}$, and $S = (-19)(-79580) - (-19)(-74810)$. Compute $\frac{R}{\text{det}} + \frac{S}{\text{det}}$. | 4,300 | graphs = [
Graph(
let={
"_m": Const(11011),
"_n": Const(2),
"num_x": Sub(Mul(Const(-74810), Const(-11)), Mul(Const(-79580), MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Ref("_n")), Divides(divisor=Var("d"), dividend=Ref("_m"))))))),
"n... | NT | null | COMPUTE | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR",
"SUM_GEOM"
] | 6cc952 | alg_linear_system_2x2_v1 | null | 3 | 0 | [
"MIN_PRIME_FACTOR",
"SUM_GEOM"
] | 2 | 0.004 | 2026-03-10T02:12:55.876980Z | {
"verified": true,
"answer": 4300,
"timestamp": "2026-03-10T02:12:55.880578Z"
} | 1aa74d | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 222,
"completion_tokens": 1295
},
"timestamp": "2026-03-29T02:21:29.062Z",
"answer": 4300
},
{
"i... | 1 | [
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "SUM_GEOM",
"status": "ok"
},
... | {
"lo": -4.31,
"mid": -1.92,
"hi": 0.62
} | ||
d207bb | comb_count_surjections_v1_784195855_2559 | Let $ S $ be the set of all positive integers $ t $ such that $ 5 \leq t \leq 20 $ and there exist integers $ a, b $ with $ 1 \leq a \leq 4 $, $ 1 \leq b \leq 4 $, and $ t = 3a + 2b $. Let $ n $ be the number of ordered pairs $ (x_1, x_2) $ of positive odd integers such that $ x_1 + x_2 = |S| $. Let $ k $ be the number... | 17,130 | graphs = [
Graph(
let={
"_n": Const(65006),
"n": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x1"), Var("x2")]), condition=And(IsPositive(arg=Var(name='x1')), IsPositive(arg=Var(name='x2')), IsOdd(arg=Var(name='x1')), IsOdd(arg=Var(name='x2')), Eq(Sum(Var("x1"), Var("x2")),... | COMB | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM/COMB1",
"COUNT_CARTESIAN"
] | 302b1d | comb_count_surjections_v1 | null | 6 | 0 | [
"COMB1",
"COUNT_CARTESIAN",
"LIN_FORM"
] | 3 | 0.005 | 2026-02-08T05:52:30.183917Z | {
"verified": true,
"answer": 17130,
"timestamp": "2026-02-08T05:52:30.188650Z"
} | fcada0 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 329,
"completion_tokens": 6339
},
"timestamp": "2026-02-24T04:47:19.676Z",
"answer": 17130
},
{
"... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COMB1",
"status": "ok_later"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_... | {
"lo": -0.06,
"mid": 2.89,
"hi": 5.27
} | ||
a62fb1 | antilemma_k3_v1_784195855_5012 | Let $d$ range over all positive divisors of $97106$. For each such divisor, compute $\phi(d)$, where $\phi$ denotes Euler's totient function. Compute the sum of $\phi(d)$ over all positive divisors $d$ of $97106$. | 97,106 | graphs = [
Graph(
let={
"x": SumOverDivisors(n=Const(value=97106), var='d', expr=EulerPhi(n=Var(name='d'))),
},
goal=Ref("x"),
)
] | NT | COMB | COMPUTE | sympy | K3 | [
"K3"
] | 54c41e | antilemma_k3_v1 | null | 4 | 0 | [
"K3"
] | 1 | 0 | 2026-02-08T07:33:31.173918Z | {
"verified": true,
"answer": 97106,
"timestamp": "2026-02-08T07:33:31.174218Z"
} | 4ad932 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 101,
"completion_tokens": 857
},
"timestamp": "2026-02-13T11:15:20.105Z",
"answer": 97106
},
{... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
}
] | {
"lo": -5.55,
"mid": -3.01,
"hi": 0.32
} | ||
c32b42 | nt_count_gcd_equals_v1_1470522791_1114 | Let $k$ be the number of ordered pairs $(i, j)$ of positive integers such that $1 \leq i \leq 3$, $1 \leq j \leq 141$, and $\gcd(i, j) = 1$. Find the number of positive integers $n \leq 6724$ such that $\gcd(n, k) = 2$. | 2,110 | graphs = [
Graph(
let={
"upper": Const(6724),
"k": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=Eq(GCD(a=Var("i"), b=Var("j")), Const(1)), domain=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(3)), right=IntegerRange(start=Const(1), ... | NT | null | COUNT | sympy | COUNT_COPRIME_GRID | [
"COUNT_COPRIME_GRID"
] | 20ec03 | nt_count_gcd_equals_v1 | null | 5 | 0 | [
"COUNT_COPRIME_GRID"
] | 1 | 0.552 | 2026-02-08T13:26:19.049271Z | {
"verified": true,
"answer": 2110,
"timestamp": "2026-02-08T13:26:19.601681Z"
} | 6d430d | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 124,
"completion_tokens": 1131
},
"timestamp": "2026-02-15T15:38:34.929Z",
"answer": 2110
},
{... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "ok"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
}
] | {
"lo": -5.49,
"mid": 0.22,
"hi": 6.51
} | ||
01796c | nt_count_coprime_v1_655260480_1521 | Let $k$ be the number of integers $t$ such that $14 \leq t \leq 120$ and there exist integers $a$ and $b$ with $1 \leq a \leq 4$, $1 \leq b \leq 20$, and $t = 10a + 4b$. Let $S$ be the set of all positive integers $n$ such that $1 \leq n \leq 10080$ and $\gcd(n, k) = 1$. Compute the number of elements in $S$. | 4,032 | graphs = [
Graph(
let={
"upper": Const(10080),
"k": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=4)), Geq(left... | NT | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | nt_count_coprime_v1 | null | 5 | 0 | [
"LIN_FORM"
] | 1 | 1.366 | 2026-02-08T16:12:28.388734Z | {
"verified": true,
"answer": 4032,
"timestamp": "2026-02-08T16:12:29.755152Z"
} | 3fd371 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 162,
"completion_tokens": 2617
},
"timestamp": "2026-02-16T22:47:55.775Z",
"answer": 4032
},
{... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "VAL_SUM_EQ",
"statu... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} |
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